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English

Renewal Notice

Kumar, Anil C P

Thangaraj, N

Indian J. Phys. 80(1). 37-41 (2006)
4 V - ^ ^
A  study of refractive index structure constant from radar data
C P Anil Kumar** and N Thangaraj^
'Elquatorial Geophysical Research Lahcnalory. Indian Instiiute of Gcomagneiism, Knshnapuram (BO),
Maharajanagar (PO). Tirunclvch^27 011, Tamil Nadu, India 
^Department of Physics, V H N S N Coll<3|ge. Virudhunagar, Tamil Nadu, India
E-mail : cpaniIC«^i^s.iigm.res.in 
Received 25 April 2005, accepted 24 October 2005
Abstract : The work focuses on the measurement of refractive index stnictuie constant from the backscatlcred signal strength. For this purpose, 
I have made use of the equatorial data mcasuicd by medium Ircqucncy (1.98 MHz.) Partial Reflection Radar, located at Tirunelveli (8.7®N. 77.8®E. 
0.3'^N magnetic dip.). This radar has been operated continuously by the Indian Institute of Geomagnetism; the data obtained with this radar have been 
providing valuable information on middle atmosphere dynamics. This is a preliminary study conducted in the equatorial region and the Partial 
Reflection Radar is not an efUoenl tool for turbulent studies, hence the estimation of refractive index structure constant of turbulence i.e, C^  ^ is very 
difficult. ITie refractive index structure constants for turbulence is calculated numerically and plotted with the vertical wind velocity. values 
show an enhancement during post sunset htmrs. It may be due to the fact that the plasma within the geomagnetic flux tube becomes unstable because 
of pre-reversal enhancement (E’ x B clectrodynamic drift) and takes part in the up-welling process thus making turbulence within the volume.
Keywords Retractive index .structure constant, turbulence, radar data.
PACSNo-s. : 94.10.Lf. 84.40.Xb
1. Introduction
Radar is a means o f collecting information about distant 
object.s by sending electromagnetic waves on them. When 
transmitted energy falls on a distant object like clouds, 
winds, eti\, it reflects back some portion o f this energy 
(echo). The reflected energy is scattered in all directions 
with intensities, a function o f object's geometry and 
object’s materials.
At the Equatorial Geophysical Research Laboratory 
(EGRL), Krishnapuram, a high-power medium frequency 
(MF) partial reflection radar was installed in 1992 under 
an Indo-Australian collaborative project, the main purpose 
being to obtain continuous measurements o f neutral winds 
in the altitude region 60-lCX) km.
2. Mathematical analysis
an antenna with radiating power P, and with the gain 
Of illuminates a target o f cross-sectional area at a
The paf>er was presented at the 11th International Symposium on Equatorial 
Acronomy (ISEA) Taiwan, May 9-14, 2005.
Corresponding Author
distance ‘ r' away from the antenna, we can write the 
incident power P, on the target as
P, = P,Cf,s/4/rr. (1)
For a monostatic radar system, the back scattered power 
received by the antenna is
PfGf a A ,L (2 )
A J l r  4 P r-
where is the effective area o f the antenna, L  is the 
efficiency o f the antenna and X is the wavelength, and
G, =  (3 )
Then eq. (2) reduces to
_  PfA^aL
(4 )
this is the standard radar equation for a single scattering 
target situated in the antenna beam. For a randomly 
distributed scatterer,
©  2006 lACS
38 C P  Anil Kumar and N  Thangaraj
PAnX -r^'cp 47TA (5)
p , a ; l
The radio refractive index o f the atmosphere v r  is 
defined as
n = (6)
where is the relative pemieability o f air for the 
atmosphere, and 4r is the dielectric constant o f the medium
m .
Again, a general formula for refractive index o f radio 
waves propagating through middle atmosphere can be 
expressed as [2]
in - 1 ) :
3.73xJ0"'<> 7.76xl0*/» - N ,
2N„
(7)
where e is the partial water vapour pressure in mbars, P  
is the total atmospheric pressure in mbars, T  is the 
absolute temperature in Kelvin, N^ . is the number o f 
density o f electrons and N^ . is the critical plasma density.
The first term in eq. (7) is the contribution due to 
water vapour, and is only relevant within the troposphere. 
The second term is due to dry air and is dominant above 
the tropopause. The third term is due to free electrons, 
and is dominant at ionospheric heights. From eq. (5), we 
have the backscatter cross section 13~5] :
o - = (4 X ?,.l4 )r*P^yP,A f.L . (8)
The relationship between the strength o f atmospheric 
radar backscatter and the intensity o f refractive index 
structure constant for turbulence has been reformulated 
as
C “ = of0,00655 X (9)
where is the potential refractive index structure 
constant and A is the radar wavelength.
More precisely, these are the clear air echoes produced 
by fluctuations o f the atmospheric index o f refraction. 
Partial Reflection Radar means transmitting signal from 
the earth is partially reflected in the E-region o f  
ionosphere and remaining signal transverses into the higher 
region o f the ionosphere. 7'hen the receiver collects the 
reflected signal from the ionosphere. The received power 
is very small as compared to transmitted power. The 
radar receiver is o f super-heterodyne type. Input o f  the 
receiver is a low-noise device which has the capability 
o f receiving weak signals. Details are given in Section
(3). The radar operating at VHF-UHF bands is mainly 
sensitive to inhomogeneities in the radio refractive index
associated with small-scale atmospheric turbulence, the 
backscattered signal can be effectively used for the 
quantification o f turbulence f5,6J.
3. System details
The transmitting array is arranged in a square, and 
consists o f four center-fed half wave dipoles, 75 m in 
length. The antennas are constructed from 3 mm pre­
stretched copper wire. One set o f dipole is arranged 
parallel to the Earth’s magnetic field and the other is 
arranged orthogonal to it. This is because Tirunelveli is 
close to the magnetic equator and the ordinary and the 
extra ordinary rays arc linearly polarized parallel to, and 
at right angles to the magnetic field, respectively. One 
set o f dipoles is used for O-mode during the day lime 
and the other is used for transmitting E-mode during the 
night time. The O-modc dipoles are oriented in the 
north-south direction. The <^-mode dipoles are oriented in 
the east-west direction. The ideal height o f the transmitting 
antenna is one quarter o f the transmitting wavelength (30 
m) above the ground plane.
The receiving antennas are o f the inverted V-iype, 
and are situated at the vertices o f an equatorial triangle 
in which the basic spacing is 180 m. The centers o f both 
the transmitting and receiving arrays coincide, making 
this truly monostatic system, 'fhe impedance o f each 
receiving antenna was 50 ohm to match the co-axial 
cable taking the signal back to the receiving system.
The transmitter operates at a frequency o f 1.98 MHz, 
although this is adjustable by -0.2 MHz, and is fully 
phase coherent. The transmitter power is 25 kW peak to 
peak, with a variable pul.se length o f 10-50 micro seconds, 
usually operated at 30 micro seconds which corresponds 
to a 4 km height resolution. The pulse repetition frequency 
is 50 Hz with 32 point integration. Super-heterodyne 
receivers are used in the system. In each receiver, signal 
o f 1.98 M Hz is mixed with a 2.475 M Hz local o.scillator 
signal to produce a 477 KHz Intermediate Frequency 
which is then fed to the signal proce.ssing unit. This 
signal is fed to phase detectors and then digitized to 16- 
bit revsolution 12]. Receiver details are provided in 
Table 1.
The Partial Reflection Radar is mainly used for 
studying wave processes; it can be inferred from the 
wind motion which is directly recorded. Wave effects on 
the atmosphere are the changes in density, temperature 
and air flow. Here, the density and temperature changes 
result in the variation o f pressure which subsequently 
results in the flow  o f  air.
A study o f refractive index structure constant from radar data 39
Table 1. Receiver details of Partial Reflection Radar.
No. .Specification Details
1 Number <^ f receivers
2 Center frequency
3. Band width (3 dB)
4 .Sensitivity
5 Maximum gain
b. CJaiii coniiol
7 Gain control range
8 Input impedance
q Signal proccs.sors
10 .Sampling starling
height
1.98 Mil/
-30 KH/
-10 )Av
60 dB
l*iogrammable in steps ol 1 dB 
60 dB 
50 12
The digiti/eis have 16-bit rest»Iinuui 
60-08 km (day): 70-08 km (night)
4. Middle atmosphere and turbulence
Wind ari.ses due to temperature, density and pressure 
gradients. Depending upon the nature and lime scales o f 
external restoring forces, different types o f wave motions 
aie produced in atmosphere. When thc.se atmospheric 
waves travel Irom one region to another region ot the 
globe both vertically and horizontally, a dynamical 
coupling is created among the different regions o f 
atmosphere 17). A .study o f perturbation in any o f the 
aforesaid parameters would be helpful in understanding 
the dynamics o f Earth's atnu^sphere loo.
d’he tropical atmosphere is inllucnced by solar radiation 
which drives both large scale circulation and cumulus 
convection. The conolis lorce is smaller, hence this 
allows certain wave modes which get trapped in equatorial 
legion. Since the gas density exponentially decreases 
with height, the atmospheric waves grow m amplitude 
upwards, and become significant contributors to the 
momentum and energy budgets o f the middle upper 
atmosphere (80-100 km).
The measured wind field over Tirunelveli (8.7 'N, 
77.8“E) exhibits variability on .several time .scales. Several 
wave events lasting for a few days to few lens o f days 
have been ob.servcd, revealing the innuence o f lower 
atmospheric wave excitation processes on the region up 
to 100 km [8-lOJ.
Tides are known for many years to play an important 
role in the dynamics o f  the middle atmosphere. 
Atmospheric tides are global scale oscillations in 
temperature, density, pressure and wind at periods which 
iirc sub-harmonics o f a solar/lunar day. Solar tides are 
primarily generated by thermal force due to absorption o f 
solar radiation by water vapour or ozone [11,12]. They 
are further classified into two : (i) migrating tides and 
(ii) non-migrating tides.
Tides have in general, amplitudes larger than other 
wave motions and they dominate in the atmospheric 
dynamics. They iiansport momentum and wave energy 
Upward Irom iheii source regions to the regions in which 
they are displaced by various instabilities such as (i) 
Inertial instability (ii) Shear instability (iii) Bart)lropic 
and Baro clinic instability and hence, affect the mean 
circulation and structure o f the atmosphere |1.3 —15|.
Many have concentrated on large scale motions w'hich 
are prevalent in the atmosphere. In fact, the most ctnnmon 
Stale ol any lluid is turbulent flow' and only some o f the 
flow can be termed laminar. It is only becau.se the 
atmosphere is turbulent that we can use partial reHection 
radar to study it in a limited manner.
rurbulence can exist only if energy available for its 
generation is greater than the buoyancy effects. The 
dclcrminatitm the structure o f the turbulence is often 
one o f tile primary objectives o f atmosphere dynamics 
studies. In that case, the velocity and density fluctuations 
can often be thought o f as being composed o f a number 
ol sinusoidal lluctuations o f varying scales, and varying 
spatial orientations. We can therefore, by analyzing the 
wind or density fluctuations, discover something about 
the spectrum o f turbulence. The energy spectrum is 
divided into three distinct regions based on the distinct 
characteristics o f turbulence within each region, known 
as the buoyancy range, inertial range and viscous range.
Middle atmosphere turbulence (80-120 km) is thought 
to be due to gravity waves and tides, which generate 
turbulence through many different processes including 
non-linear breaking, shear instabilities, convective over­
turning, and critical level interactions. Turbulence is 
important becau.se it is a large contributor to the diffusion 
of momentum, heat and matter. Meso.sphcric turbulence 
can be both spatially and temporally intermittent and 
may occur in patches or in horizontal layers. I'hc layers 
may be upto several kilometers thick and may be in a 
‘sandwich'-type arrangement such that the turbulent layers 
arc bound by non-turbulent regions. Around an altitude 
o f 110 km, the molecular vi.scosity becomes large enough 
to damp out any turbulence, and this region is referred to 
as the turbopausc. While turbulence in the neutral 
atmt^sphere has been observed to heights o f -130 km, 
above the turbopausc it only plays a minor physical role.
4'urbulcnce is one o f the primary generators o f both 
spatial and temporal variations in the refractive index o f 
the atmosphere; it creates a medium which scatters 
electromagnetic radiation thereby enabling one to probe
40 C P Anil Kumar and N  Thangaraj
the almospherc and study both the long-term and sliort- 
lerm dynamics as well as turbulence itself.
5. Rei'ractivc index structure constant
In the thet)ry o f electromagnetic wave propagation in 
turbulence, the refractive index structure constant is taken 
as a measure o f the strength o f the turbulence. A  lot o f 
efforts have been made to measure this parameter at 
different regions and seasons. However, this parameter 
docs not indicate the fluctuation strength directly. It is 
found that the strength o f turbulence is the variance o f 
the refractive index. In the inertial sub-range, the structure 
function o f refractive index generally depends on both 
the variance and the turbulence outer scale 13).
6. Methodt)logy
This is a preliminary study conducted in the equatorial 
region and since the Partial ReHection Radar is not an 
efficient tool for turbulent studies, the estimation o f C,p is 
very difficult. However, this paper tried to develop a 
method to derive profiles from available high resolution 
partial reficction radar data. To simplify the analysis, wc 
make the assumption that there are no errors in the radial 
velocities and the radial velocity terms have been perfectly 
converted into horizontal components. Starting with the 
horizontal components, there is an in-built post-processing 
software to compute the horizontal divergence at each 
level which is then integrated to get the vertical velocity. 
Software program has been developed based on the eqs. 
(8) and (9) to compute C,f values from the received 
signal power {P^), Radar can measure the refractive index 
structure function, because C„“ is proportional to the radar 
reflectivity fl2 ].
C ; =
where // is the radar reflectivity and A is the radar 
wavelength.
7. Results and discussion
Data from first January 2005 to thirty first January 2(X)5 
had been taken for the present analysis. 24 hours data is 
used for the evaluation o f Partial Reflection Radar 
normally provides information from 80—110 km, for the 
sake o f computation windowing is done between 80-88 
km ranges. The receiver-1 value is given asC^^ and 
rcceiver-2 values are given as C^2* ^  comparative study 
o f different C l (average) has been made for this equatorial 
station.
The values were studied to see what activity 
proceeded in the thermosphere during the sun set and sun
rise hours in this zone. 7b show the effect, we selected 
three type viz. severe, moderate and weak having different 
C,7 values. It was found that most o f the days showed 
the post-sun.scl peak at 20.(X)-2l.(X) 1ST as depicted in 
Figure 1. The figure depicts the refractive index structure 
constant C “,, C„2 and vertical velocity (data o f 1st January 
2005); both and C„ 2  shc)wed an enhancement.
Moderate C~ values were al.so observed on 15th, 17th 
and 20lh January as shown in Figure 2. The minimum 
values were noted in rare cases and depicted as such in 
Figure 3.
Hetractive tniiex structure constant
10'"^  10- 10- 10- 10”
Figure 1. The refractive mdex .structure constant f ( a  ). and vertical
vclocuy (— ) [data from partial reflected echoesl.
Refractive index structure cor^stant
VfcRTICAL V t lO C IT Y  (m/s)
Figure 2. The retractive index structure constant •) and vertical
velocity (— ) (data from partial rcllccted echoes].
Refractive index structuro constant
lo ‘* 10*'
VERTICAL VELOCITY (m/a)
Figure 3. The refractive index structure constant and vertical
velocity (— ) (data from partial reflected echoes].
A study o f refractive index structure constant from radar data 41
The study reveals that the association between the 
refractive index structure function C,^  is proportional to 
the radar reflectivity. The quantification of lurbulence in 
this regime may provide the Physics of E-Iayer dynamics 
after the post-sunset hours. However, the detail 
examination and classification of the cause will requiie 
further investigations.
8. Conclusions
A study of radar based measurements of is carried out 
in this paper. The determination of the refractive index 
structure constant of the turbulence is often one of the 
primary objectives in any study of turbuicnce. In the 
ihci^ry of electromagnetic wave propagation in turbulence, 
the refractive index structure constant is taken as a 
measure of the strength of the turbulence. 1 he lefraeiive 
index structure constants for turbulence is calculated 
numerically and plotted with the vertical wind velocity. 
c l  values show an enhancement during post-sunset hours. 
It may be due to the fact that plasma within the 
geomagnetic flux tube becomes unstable because of pre- 
reversal enhancement (E x B electrodynamic drift) and 
take part in the up-wcIling process thus creating turbulence 
within the volume.
Acknowledgments
The authors would like to acknowledge the critical
comments from the referee wliich enabled a better 
presentation o\' the paper. Tins research work is supported 
by the Department of Science and lechnology. Govt, of 
India.
KfiViTiices
111 UK lican anil I'. J Duilon Riulin Mctenmldi^v (New '^ 'ork . U»>vci) 
(196X)
\2
D
|4
|7
|9
HO
Hi
I12
H-^
H4
H5
Dra/cii Losicar PhD JhcM\ (Univcrsily of AdclaickO I 
W K I locking AJr Sfuac Rrs 7 17I (19S7)
W K Hoiking/\^A .S>/cc Rc  ^ 1 2 2 0 7 ( l W )
W K Hoiking J Atmos Ictn /Vma. 45 SO (1983)
D Naiayana Rao, T  N Rao. M Vcnkalarainam, S I Imlasuaman, S V 
U Rao, P Snmvasalu anil 1* B Rao Radio. Su 36 1439 (2001 )
S Kato Developments in hiuth iind Planetatv Si'icm es (Tokyo . 
D R oidcl)(l9S0)
S Guinharan and R Kajaiam ./ Geophxs Res 106 31817 (2(K)l)
R Rajarum and S Gurubaran Ann Geophw 'n ae 16 197 ( 1998)
S Gurubaran and R Rajaiam Geophy. Res. U'tt. 2 6  1113 (1999)
B 11 Biiggs, G J Phillips and H H Shmn I*ror, Phvs. S o< . (London) 
63B 1 0 6 (1 9 5 0 )
11 OUcistcn Radio Sl /. 4 1179 (1969)
R S Licbcrman and I* B H.iys ./ Atmos. Si i 51 3094 {1994)
J M forbes and F Vital J Atoms terr Phy 51 649 (1 98 9)
J M Forbes /  Gcophs's. Res. 87 5222 (1982)


A Study of Refractive Index Structure Constant from Radar Data

Yadav, R K

Shanker, R

Relative Backscattering Yields for Electrons and Positrons from Tungsten at Kev Energies

Yadav, B S

Kumar, Nitin

Singh, Manoj Kumar

Indian J, Phys, 80 (1), 61-65 (2006)
F T IR  absorption spectra and thermodynamic functions o f 
5-chloro-2,3-dihydroxy pyridine
B S Yadav*, Nilin Kumar, Manoj,Kumar Singh and M K Yadav 
Molecular Spectroscopy and Biophysics Laboratory, D ijl (PG) College, Mccrut-250 CKJ2, Uttar Pradesh, India
Received 25 April 2005, accepted 24 October 2005
Abstract : The infrared absorption spectra of 5-chloro-2,3-dihydroxy pyridine have been recorded in the region 400 — 40(K) cm 'I’he bands 
observed in the IR spectra arc discussed by assuming the compound under C, point group symmetry. The modes of vibration for the different 
fundamentals have been propc^sed. The thermodynamic functions have also been calculated by using IR frequencies at different temperatures with 
the help of computer programming.
Keywords : Infrared and Raman spectroscopy, vibrational frequencies, thermodynamic functions.
PACS Nos. : 33.20.Ea. 33.20.Fb
1. Introduction
The aromatic compounds like benzene, benzaldehyde, 
pyridine, pyrimidine, uracil, cytosine and their derivatives 
arc o f great biological importance as they play an 
important role in the structure and properties o f nucleic 
acids [1—6]. The vibrational spectra o f di-substituted 
pyridines have been studied by some worker [7,8], but 
very little work appears on the IR spectra o f iri-substitutcd 
pyridines [9,10). Further when the N-hetcrocyclic 
molecules have some substituent like -OH, -SH and -NH^, 
they may cause tautomerism. In view o f these, we discuss 
the vibra-tional spectra o f 5-chloro-2,3-dihydroxy pyridine.
2. Experimental
Speepure grade chemical 5-chloro-2,3-dihydroxy pyridine 
was obtained from M/S Aldrich Chemie, West Germany 
and used as such. This chemical hereafter, referred as 
5,2,3-CDHP. The purity o f the said compound was also 
confirmed by elemental analysis and melting point 
determination. The infrared absorption spectra o f 5,2,3- 
CDHP was recorded on Perkin Elmer spectrophotometer 
model-52 in the region 400-4000 cm'^ using KBr pellet. 
C^orresponding Author
3. Results and discussion
I ’hc structural formula o f the compound 5,2,3-CDHP is 
given in Figure 1.
OH
OH'
Figure 1. Molecular structure of 5-chloro-2,3-dihydroxy pyridine.
The IR spectra o f 5,2,3-CDHP in KBr pellets is given 
in Figure 2. The fundamental vibrational frequencies o f 
the said molecule are given in Table 1. The C, point 
group symmetry has been assumed for the analysis o f the 
said molecule. The thermodynamic parameters viz. free 
energy function (F*" -  Ej)/r, entropy function 5'", enthalpy 
function (F °  -  E^/T, and heat capacity function with 
absolute temperature are given in Table 2 for 5,2,3- 
CDHP. The variation o f free energy and entropy function
© 2006 lACS
62
Tabic 2. Thermodynamic functions of 5,2,3-CDHP (Cal./Mole-K).
U S Yadav, N it in  Kumar, ManoJ K um ar Singh and M  K  Yadav
Table 1. Assignment of vibrational frequencies m (cm ') of 5,2,3-CDI IP,
IR Assignment
431 vw (O-H) torsion, yiing
520 w P iC -O ),  yring
565 ms /?(C-OH)
626 w Turing
676 ms P {C -0\\ )
782 w ring breathing, C-N-C bending vibration
814 w r(C -H )
846 ms trigonal bending
904 w (C-C-C) trigonal bending
959 ms (C-C-C) trigonal bending, r(C -C l)
1106 w
1177 s p{CA\ )
1309 ms t'(C-OH)
1341 s i/(C-OH)
1427 ms luring ’
1450 ms luring
1571 s pring
1611 s prmg
1677 s p(C=0)./?(N-H )
3103vw P(C-H )
3111 vv P(O-H). P(C-H)
3237 w P(O-H)
3266 vw Kym.(N-H)
Stretching,
P  = in-plane bending.
Y~ out-of-plane bending, 
Kym.* symmetric stretching.
vw = very weak, 
w = weak,
ms = medium strong, 
s =s strong.
Temperature
(K)
-(/=" -  t:^VT ~-{tr -  E tvr  ^r
2(K) 59.29 21-47 12 78 21.47
300 65.28 29.12 16.99 29.12
400 70.71 35.66 20.80 35.66
500 75.75 41.20 24.40 41.20
600 80.48 45.79 27.59 45.79
700 84.96 49.59 30.47 49.59
8(K) 89.20 52.75 33.06 52.75
9(X) 93.23 55.-39 35-40 55.39
KKX) 97.07 57 61 37.51 57.61
IKK) 1(K).74 59 49 39.43 59.49
121K) 104.25 61.08 41.17 61.08
13(K) 107.61 62.44 42.75 62 44
14(X) 110.83 63.61 44.20 63.61
15(X) 113.93 64.61 45-53 64.61
.S’" = entropy, = free energy, Cy = zero point energy, (//" -  L'H) ~ enlhalp> 
- heal capacity.
••— Enmoy
with temperature is shown in Figure 3, while that o f 
enthalpy and heat capacity function with absolute 
temperature is shown in Figure 4 for 5,2,3-CDHP.
JOO 3(X) 400 .MK) <iOn 700 KOO l(X » IUNII?(X) 1 VXl 1400 ISOCI lemperaiure (K>
Figure 3. Temperature vs. free energec and entropy for 5,2,.3-CDHP.
3.7. Vibrational spectra :
3.L I ,  Ring vibrations :
3,1,1.1, C -H  Vibrations :
Since the molecule 5,2,3-CDHP is a tri-substituted
F T IR  absorption spectra and thermodynamic functions o f 5-chloro-'2^3~dih\droxy pyridine 63
pyridines, it has two hydrogen atoms left around the 
ring. Thus, the compound 5,2,3-CDHP may have two C- 
H valence oscillations which usually lie in the region 
3000 - 3 100cm'‘ [11]. Two IR bands have been observed 
at 3103 cm * and 3111 cm ' which have been assigned to 
this mode. These assignments are also in agreement with 
the literature value fl21. Rao [13] has suggested that C- 
H in-plane and out-of-plane bending modes lie in the 
region 1000 -  1250 cm * and 700 -  900 cm *, respectively. 
Gupta et al [141 have assigned C-H in-planc bending 
mode at 1124 cm ‘ in 4-hydroxy-3-methoxy benzaldehyde 
and out-of-plane bending modes at 790 and 828 cm ' in 
3-hydroxy-4-methoxy benzaldehyde while GocI and Atrey 
[151 have assigned C-H out-of-plane bending mode at 
1245 cm ’ in 3-amino-2-chloro pyridine. Tripathi and 
Pandey [9J have assigned these modes in the region 
1015 -  1180 cn r ‘ and 805 -  895 cm * in hydroxy pyridine.
In view o f these assignments, the bands ob.servcd at 
1106 enr* and 1177 cm * have been taken to represent 
in~plane bending modes while the bands observed at 814 
cm * and 846 cm * have been taken to represent C-H 
out-of-plane bending modes. These assignments are also 
in agreement with the literature values [16,17|.
J L I .2. C-C, (S~N and N -H  vibrations :
In benzene and substituted benzene, the frequency o f 
ring breathing mode have been assigned in the region 
690-844 cm * [12,13|. The IR band observed at 782 cm * 
has been assigned to ring breathing mcxle in the present 
investigation. The C-C stretching, in-planc and out-of­
plane bending modes have been assigned in their 
respective regions [12,13] (Table!). The C-C-C trigonal 
bending vibrations have been assigned at 904 cm * and 
959 cm * while C-N-C trigonal bending vibration has 
been assign at 782 cm * which are in agreement with the 
literature values [12,13,18],
Due to the tautomeric behaviour o f the molecule, the 
N-H streching frequency may appear in the molecule. Vir 
Singh et al [5] have assigned this mode at 3230 cm * in 
2,4-dihydroxy-6-methyl pyrimidine. In view  o f this 
assignment, a weak IR  band observed at 3266 cm~* has 
been assigned to N-H streching mode o f vibration while 
the band observed at 1677 cm"* has been assigned to N- 
H in-plane bending mode o f vibration. This also finds 
support from the literature [8,15], Various other modes 
have also been assigned in Table .1 in their respective 
regions 113,19].
3.1. L3. C -X  vibrations :
Some workers [20,21] have assigned (C-OH ) stretching 
mode around 13(X) cm~* in substituted benzene. Gupta et 
al [14] have assigned this mode at 1262, 1265 and 1270 
enr* in hydroxy methoxy benzcldchyde, while Yadav 
et a! 1221 have assigned this mode at 1270 cm * in the 
identical compound.
In view o f these assignments, the bands observed at 
1309 cm~‘ and 1341 cm ' have been assigned to this 
mode. 7 he (C-OH) in-planc bending modes have been 
assigned at 565 cm * and 676 cm ' in the compound 
5,2,3-CDHP.
; Goel and Agarwal [231 have assigned (C -C l) streching 
inode at 1065 and 1055 enr* in 3-amino-2-chIoro pyridine 
and in 5-cliloro-2,4-dimethoxy aniline. In view o f these 
assignments, the band observed at 959 cm * (K B r) has 
been taken to rcpre.scnt (C-CI) stretching mode in 5,2,3- 
CDHP. Since the compound is a hydroxy- substituted 
pyridine, so the hydrogen atom o f the hydr<>xy group at 
position 2 migrates to the N-atom o f ring which shows 
the existence o f C =0 , N-H streching and bending modes.
Vir Singh et al [8] have assigned a medium strong 
band at 1700 cm ' in 2,4-dimethyl-6-hydroxy pyrimidine 
to represent (C = 0 ) streching mode o f vibration and 
(C = 0 ) in-plane and oul-of-planc bending mode at 530 
and 360 enr* in the same molecule. In view o f this, the 
strong IR band at 1677 cm * has been assigned as (C = 0 ) 
streching mc^dc o f vibrations, while the IR band observed 
at 565 cm ' has been assigned as (C = 0 ) in-plane bending 
mode o f vibration. Both the bands are taken in KBr 
pellet techniques.
3.1.2. Cjroup vibrations :
3.1.2.1. OH f'roup :
In monomeric phenols [24], the -OH stretching mode 
appears around 36(X) cm * whereas in associated species 
[14,25], it is reported in the region 3145—3430 cm *. 
Goel et al [28] have assigned this mode at 3560 cm"* in 
4,6-dihydroxy-2-mercapto pyrimidine. In view o f  these, 
the bands observed at 3111 cm"* (K B r) and 3237 cm"* 
(KBr) have been taken to represent O-H stretching modes.
The spectra o f substituted benzene shows the O-H 
torsion mode as usually a weak band [13]. Goel and 
Agarwal [23] and Siquenza et al [26] have assigned this 
mode near 420 cm"' in penta-chloro-phenols, while Faniran 
[27] have assigned this mode at 314 and 318 cm~‘ in
64 B S Yadav, Nitin Kumar, Manoj Kumar Singh and M  K  Yadav
penta-bromo and penta-chloro-phenols. During the presents 
investigation, these modes have been identified at 431 
cm"'. The various other modes o f this group have been 
assigned in their own regions in the Table 1.
4« Thermodynamic functions
The thermodynamic parameters viz. heal capacity C°, 
enthalpy (H^ -  and entropy function S° o f the
compounds 5,2,3-CDHP have been computed by using 
the standard expressions [28,29] by taking X-axis to pass 
through the para position and Y-axis perpendicular to 
m olecular plane. For determ ining the rotational 
contribution, the structural parameters give in Table 3 
were used [30,31].
- Enthalpy
- Haat Capactty
TEM PERATUne (K)
Figure 4. Temperature vs. f^ ree energee and heat capacity for 5.2,3<CDHP.
The thermodynamic functions have been calculated at 
different temperature between 200—1500 K by using (3/i- 
6) fundamental frequencies for the said compound and 
assuming rigid rotator harmonic oscillator approximation. 
The calculations were performed for one mole o f an 
ideal gas at one atmospheric pressure. The symmetry 
number for overall rotation and internal rotation has been 
taken as two. The principle moment o f inertia were 
found to be 0.3863, 0.8615 and 1,2478 x 10“^^  gm cm^ 
for the said molecule. A ll the thermodynamic parameters
are plotted as function o f temperature (Figures 3.4), 
From graphs, it was found that all the thermodynamic 
parameters rise more rapidly in the low temperature 
range and less rapidly in the high temperature range.
Tkble 3. Structural parameters.
Bond length (A) Bond angles (**)
N.C, = 1.43 ^  NjCjCj = 120“
CjCi = 1.33 ^  C2C3C4 = 120“
C^ C4 = 1.32 ^C3C4C5 = 120“
C4C5 = 1.39 -iT C4C5C6 = 120“
- 1.39 ^C sQ N , = 120“
CftN, = 1.38 = 120“
C2O7 = 1.35 ^N,C207 = 121“
C,Og = 1.43 ./C 3C2O7 = 119“
C5C19 1.75 = 122“ 
^ C 4C30« = 118“ 
^C4C5C„ =118“ 
^  CftCsC,, = 122“
At very high temperature greater than 1500 K, the 
influence o f  anharmonicity wil l  be large and the 
expressions used for the calculation will not give an 
accurate value o f thermodynamic parameters. The trend 
o f variations o f thermodynamic parameters is similar to 
those reported for the similar molecules in the literature 
[32-35].
This study has become more relevant in view o f its 
great biological importance and the thermodynamics will 
used as an important tool, in the field o f research.
References
11] G T Martin Biological Antagonism (New York : Blakiston) (1951)
t2) B S Yadav. Vipin Kumar and M K Yadav Indian J. PureAppL Pltvi 
36 557(1998)
[31 N K Sanyal. R K Goel and M L Agarwal Indian J. Pure Appl. Phys 
19 480(1981)
[4] B S Yadav. Seema. Vipin Kumar and U K Jetley Indian J. P u re  
Appl. Phys. 35 587 (1997)
[5J Vir Singh. Vipin Kumar. M K Yadav. Seema and B S Yadav O rie n ta l  
J. Chem. 12 267 (1996)
[6] B S Yadav. Vir Singh, M K Yadav and S Chaudhary Indian J. Phys 
35 305(1997)
17] Narasimha. H A Yachit. K Suryanarayana Rao and M A S h a s h i d h a r  
Indian. J. Pure Appl. Phys. 23 225 (1985)
[8] Vir Singh, Vipin Kumar. M K Yadav. B S Yadav and Seema Asim J- 
C/iem. 9411(1997)
[9] R S Tripathi and B R Pandey Indian. J. Pure Appl. Phys. 13 416 
(1975)
[10] R K Goel. Rohitashva and S N Sharma Indian J. Pure Appl. Phys. 
17 187(1979)
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j j j j N Malaga and T Kubolo Molecular and Electronic Spectra (New 
York : Marccl*Dckkcr Inc) (1970)
fl2J L J Bellamy The Infrared Spectra of Complex Molecule.^  (1975) 
(London ; Chapmen and Hall)
(13j CNR Rao Chemical Applications of Infrared Spectroscopy (New 
York: Academic) (1963)
[14) S P Gupta, C Gupta, S Sharma and R K Gocl Indian J. Pure Appl. 
Phys. 24 111 (1986)
f 15] R K Gocl and C P Atrey Indian J. Pure Appl. Phys. 20 598 (1982)
1161 R K Goel, S K Gupta and S N Sharma Indian J. Pure Appl Phys. 18 
928 (1980)
117) Nitish Kr Sanyal, R K Goel, K P Kansal and S N Sharma Indian J. 
Pure Appl Phys. 18 302 (1979)
118 j B S Yadav. Vipin Kumar, M K Yadav and I R Yadav Acta Botanica 
Mica26 15(1998)
j 19) K Nakamolo / R Spectra of Inorganic and Coordi nation Compounds 
(New York : Wiley-Inierscience) (1970)
(20J B S Yadav. Vir Singh, Vipin Kumar and M K Yadav Asian J. Chem. 
9 372(1997)
121 ] SI. Sri vastava and M Prasad Spectrochim. Acta 40A 1101 (1984) 
(22) B S Yadav, Vipin Kumar, Vir Singh and B S Semwal Indian J. Pure 
Appl Phys. yi 34(1999)
[231 R K Goel and M L Agarwal Acta Phys. Polon. 61A 1017 (1982)
[241 J H S Green, D J Harrision and W Kynaslon Spectrochim. Acta 27 
2199(1971)
[251 Vipin Kumar PhD 7'hesis (CCS University, Meerut, India) (1999)
[261 C Siquenza, P F Gonzolcdiaz apd S Cifucntes J. Molec. Struct. 72 
165 (1981)
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Van Nostrand-Reinhold) (1966)
[291 B S Yadav, Vipin Kumar, Vir Singh, M K Yadav and S Chand huTtan 
J. Phys. 72(B) 183(1998)
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Chemists 69 5 (1997)
IS1J CL Chaterjee, P P Garg and R M P Jaiswal Spectrochim. Acta 39A 
943 (1978)
[321 JO Hirich felder, C F Curtissand and B B Bird Molecular Theory of 
Gases and Liquids (New York : John Willey) 1954
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[351 J Turkevich and P C Stevenson J. Chem. Phys. 11 328 (1943)


FTIR Absorption Spectra and Thermodynamic Functions of 5-Chloro-2,3-Dihydroxy Pyridine

Bandyopadhyay, K

Rakshit, G

Indian J. Phys.90{l\ 67-70 (2006)
Leptonic C P  violation and neutrino mass in a three generation SU(2)„
gauge model
K Bandyopadhyay^.and G Rakshit'
Department of Physics, R S P (P G ) College, (A  constituent unit of Vinoba Bhavc University, Hazaribagh)
Jhuria, Dhanbad-828 1 If, Jharkhand. India 
'Kendriya Vidyalaya No. II, Kaksha Vihar* Pon Blair-744 103, Andaman, India
H-inail : kbph^'r0diffinail.com 
Received 12 July 2004, accepted 6 September 2005
Abstract : We have shown that with suitable Higgs field the lepton muss matrix in SU(2)^ '^>c S(J(2)^x x SU(2)„ gauge model
IS identical with the mass matrix ansatz based on the permutation symmetry. The possibility of leptonic CP violation is discussed in terms 
of CP-violating rephasing-mvariunt quantity . The neutrino ma.ss bounds arc also mentioned on the basi.s of the mass matrix obtained.
Keywords: CP Violation, neutrino mass, horizontal symmetry.
PACS Nos. : 14.60.Pq, ll.30.Er, 11.30.Hv
1. Introduction ■
Although the Standard Electro-weak model [1] correctly 
describes weak interaction phenomenology at presently 
available energies, but the quark and lepton masses and 
flavour mixing angles are not predictable. Within the 
standard model, all masses and flavour mixing angles are 
free parameters and no relations among them are provided. 
Perhaps, a new theory could predict all masses and flavour 
mixing parameters in terms o f some new, few fundamental 
parameters. Recent neutrino experimental results and 
cosmological observations [2] show evidence for non-zero 
neutrino mass and provide possibility o f lepton flavor 
mixing. The standard model then has to be enlarged and 
we have more free parameters to describe the fermion 
masses and mixing angles. Although non-zero neutrino 
masses and mixing can be interpreted as the solution to 
the solar [3] and atmospheric [4] neutrino anomalies, the 
present experiments do not provide the values o f neutrino 
masses and mixing angles in three neutrino oscillation 
scheme. The vacuum oscillation and small angle M SW
‘Corresponding Author : Dr. K Bandyopadhyay, 1/D, Bibhuti Apart­
ment, Luby Circular Road, Hirapur, Dhanbad-826 001, Jharkhand, India
solutions o f solar neutrino data are also disfavoured by 
the current data. The solution for solar neutrino deficit 
may be either small or large mixing with different mass 
squared differences depending on M SW  effect [5] and 
hence, we can almost estimate the neutrino mass hierarchy 
and their mixing in extended gauge model. In this context, 
horizontal interactions among the fermion families have 
been introduced to restrict the independent parameters o f 
fermion mass matrix and to obtain some insight on the 
problems o f fermion family repetition. Several horizontal 
symmetries have been introduced by different authors 16] 
to understand the generation problem o f fermions including 
their masses, mixing angles and CP violation.
In the present work, we focus our attention on neutrino 
mass, lepton mixing as well as leptonic CP violation in the 
SU(2)^ X SU(2)jf X U(l)g_^  X SU (2 )„  horizontal gauge 
model. Our analysis shows that in the three generation 
left-right symmetric SU(2)ff model, the neutrino mass matrix 
is identical with the mass matrix ansatz based on the 
permutation symmetry with the suitable choice o f  Higgs
<e)2006IACK3
68 K Bandyopadhyay and G Rakshit
field. The CP violating phase in three generation SU(2)ff 
model lies in the range 0 < < n!2 where =  S is
considered.The value o f j [p  is approximately equal to 1.3 
X 10'^ [2] and it is small compared to large mixing angle 
(L M A ) MSW  solution or vacuum oscillation (V O ) solution. 
The bounds on neutrino masses are also discussed and 
the results arc consistent with the recent experiments [7].
The plan o f the paper is as follows. In Section 2, we 
present our model and the parameters for lepton mass 
matrices entering in the model and Icptonic CP violation 
also. In Section 3, we summarize our analysis. Section 4 
contains our conclusions.
2. Lepton mass matrices and Icptonic CP-violation
We consider a three generation left-right symmetric model 
with SU(2)f^ as the horizontal symmetry [6] based on the 
gauge group SU (2 )i x SU(2),i x U(1)n.,i x SU(2)f,. 
Besides their usual representations under SU(2)^ x SU(2)f^ 
X the left-and right-handed fermions under SV(2)i,
transform as triplets for the three generation model. The 
representation contents o f the fermions as well as Higgs 
field with their V E V ’s under SU (2 )i x SV(2)f^ x U (l)ff  ^
X SU (2 )„  are :
and right-handed and horizontal gauge bosons* r; gives 
masses to the horizontal gauge bosons and an*
introduced to break the left-right symmetry.
The most general renormalizable Higgs potential o f the 
model is
^ + Va
V. (81
(1,2,-1,3)^
(I)
^  ^ nA ^   ^ 0 X
The minimization o f the Higgs potential leads to
1^2 ^ 0, ,^3 = 0, >1'22 = 2^3 ^ '^33 =
= 0, k\. ^  0, ^',3 = 0, k\^ = 0, ^ 0, X:'33 = 0.
(9)
P \ \  = 0, /?22 ^  0, ^  0, //|1 = p 2 2  ^  P33
and a,j == a%j.
The most general and basic lepton-Higgs interaction is 
L  = /, yra,i)/>P^4>“a P  + f 2 Vr‘ce,¥^P^ x ‘‘ ccP + h.c,
( 10)
/>■ = 1, 2. 3 and (x, f t  = 1 ,2
The couplings /, and are independent o f .S7/(2)^, SV{2)j.. 
SU(2)f^f indices and hence* they are real numbers. In tins 
model* we obtain the mass matrices for both neutrinos and 
charged leptons* which have the following form
VEV's o f the Higgs fields are :
'' k,j exp (i0 ,j)
0 ^  ^ 0 02 0 '
(2)
= >^1 <^'1 and M  = CI2 '^2
0 0V C2 )
> (2,2.0,5) =
/* 7 = 1 ,  2*3
> (2 .2 ,0 ,3 ) =
0
P,j c x p ( ia , j)
0  ^
ky exp ao^j) ^
p'j expC iap
< r/ > (1,1,0,3) = /i* exp ) ,
< > (3.1,2,1) =
< 4^ > (1,3,2.1) =
(3)
(4)
(5)
(6)
(7)
(I I )
where a^  — k^  ^ exp = p^^exp
c, = exp
r/, = /^jexp (lor,,)* = 7''.exp
= k'^  ^ exp (/(2j3), d^  = Pyy^^P (*^ 33) ’
The parameters b^ , Cj, d^  ^ and a ,^ c ,^ d^  can be
expressed in terms o f fermions mass eigen values and one 
free parameter it is seen that even i f  the phases 
and are removed by redefining the fermion fields, no 
change in the results will occur. The parameters can be 
expressed as follows :
Wc have chosen the minimal set o f Higgs fields where (p 
and X  generate masses o f the basic fermions and the left-
<2j = yj2m^ni2 , b^  =  W3 / 2 | 1 + 2 .
mo — m,
my
Lcptonic CP violation cincl neutrino mass in <i three generation SU(2)i^ gauge model 6 9
r, “  W3 /2 | 1 ~-
/7?3
d^  ~ /W3 / 2
and
= yjni .^m^  ^ ^ 2  ~  . c*2 ~ yjc^m^ ,
The expressions for /;,, r ,^ are written considering 
the fact that the charged lepton family has the mass 
hierarchy m^ , < < m^ < < mr- We can take the mass eigen 
values m .^ and m, to get the fermion mass matrix, fhe 
mass matrices for charged leptons and neutrinos have the 
same fonn and the free parameter i ' '  is taken to be identical 
in both the charged lepton and neutrino mass matrices and 
ean be determined from the neutrino experimental results.
The mass matrices are complex symmetric in both the 
sectors o f leptons. The lepton flavour-mixing matrix in the 
standard parameterization can be given as
•"CKM
^2^13
” *^ 12  ^23 ^ 'l2 ‘^ 23‘^ 13
•^12 -^23 “  ^'12^'23‘^13 t."Xp(/V^, 3 )
•''12 ^ ‘13
<^^‘l2<'*23 "  •'V2-''23 ' l 3  C X p C /V ) ,^ )  
2*^ 23 ‘''12*'23*^ 13 (^ 1^3 ^
a', 3 exp(~iV>,3)
*^ *23*^13
where .s = sin O and c — cos O {i, j ~ 1, 2, 3).
The mixing angles can be expres.sed in terms o f mas.scs 
of the leptons and after constraining [2j the lepton mixing 
matrix will lake the approximate form as
H-km =
.v,2
2^ *23
*^ 12“^23
3i3 CXp(-/6'i3)
2^3
It is to be noted that the mixing matrix contains non-zero 
rP-violating phase. The value o f CP-violating rephasing- 
nvariant quantity «  1.3 x 1(T  ^ for 0 < < 7d2. For
^2 < < zr, the value o f 7^ 1^ , is much more suppressed.
However, compared to quark sector result 7/,,. is large and 
lence, lepton number violating CP violation may be indeed 
large.
The form o f the mass matrix provides [21 numerical 
v'alucs o f the neutrino mass eigen values, although they 
are not exact. But some possible ranges can be estimated. 
If wc assume the mass hierarchy o f the value
3f 4.7 X lO"  ^ eV  in case o f atmospheric neutrino. In 
large mixing angle (L M A ) solution, m, = and the
allowed neutrino mass bounds arc : 3.0 x 10^ < w, < 2.0 
X 10-' cV and 2.7 x 10  ^ < m^< 1.5 x lO'- eV for 5 x KT  ^
< I  ^ < 4 X 10 c V ‘ with -  arc tan With
the mass hierarchy m ^ «  m ,^ 1.3 x 10 ‘ < < 2.4 x
10 " cV, For large mixing between and mJ2 and
f?i,, m ,«m ^ [2 \  In case o f vacuum oscillation (V O ) solution, 
the lower bounds o f neutrino masses are m, > 0.24 x 10 '' 
cV, /?7, > 0.93 X 10 ' cV. The mixing angle can al.so he 
determined using m^  and m, [2J. In case o f small mixing 
angle (vSMA) solution, m, may have small mixing angle 
Value without a lower bound, whereas the upper bound 
depends upon CP violating phase and it ranges from, 
j.O X 10 ’ eV to 4.2 x 10 cV. The lower mass bound o f 
IS -  1.9 X 10 ' cV [21.
3. Summary
Wc have studied neutrino masses and mixing in the three 
generation left-right symmetric horizontal gauge model with 
SU(2)^^ as horizontal symmetry. The mass matrix we 
obtained after minimizing the potential containing minimal 
Higgs field, is similar to the mass matrix ansatz as given 
in Ref. 12]. Ih e  model suggests the mass hierarchy r/i, ~ 
m, «  m^  to support the L M A  and V O  solution and also 
the hierarchy /;/, «  ///, «  ni^  for SM A solution. Although 
the vacuum oscillation and small mixing M SW  solutions o f 
sedar neutrino data are disfavoured by current data but our 
motivation to show leptonic CP violation is still favoured 
because o f non-violating rephrasing invariant quantity 7/.^ . 
The magnitude o f CP-violating rephrasing-invariant quantity 
7^ .^.,, depends on the CP-violating phase angle and the 
value may be upto 1.3 x 10
4. Conclusion
We thus conclude that extended gauge model with SV{2}^^ 
horizontal gauge group for three generations o f leptons 
may give rise to leptonic CP-violation which may be large 
compared to that in the quark sector. Furthermore, the 
model gives rise to the mass matrix ansatz, which supports 
the possible bounds on neutrino masses also. Thus, SU{2)^^ 
gauge symmetry contributes to non-zero neutrino mass 
unlike the standard model and also excludes the heavy 
right-handed neutrino. It is therefore, interesting to study 
the other horizontal gauge group also [8].
References
(1) P Lungackcr Phys. Rep. 72 186 (1981); Comments Nucl. Part. 
Phys. 19 1 (1989)
(21 S K Kang, C S Kim and J D Kim Phys. Rev. D62 073011 (2000) 
and references therein


Leptonic CP Violation and Neutrino Mass in a Three Generation SU(2)H Gauge Model

Joshi, Meenakshi

Gupta, B R K

Temperature Dependence of Adiabatic Elastic Moduli of (Mg1-x, Fex)2SiO4

Iiulian J. Phys. 80 (3). 315-318 (2006)
q A ^ o t u s  f o r  C o n t r i b u t o r s
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[c] U Fano and A R P  Rao A tom ic Collisions and Spactra (New York : Academic) Vol 1, Ch 2, Sec 4, p 25 (1986)
[7] T  Atsumi, T  Isihara, M Koyama and M Matsuzawa Phys. Rev. A42 6391 (1990)
[11] T  Le-Brun, M Lavolled and P Morin X -ra y  and inner Shell Processes  (AIP Conf. Proc. 215) (eds) T  A Carison, M O Krause an 
S Manson (New York : AIP) p 846 (1990)
[14] SB Hansen, K B MacAdam and L G Gray J2th Jnt. Conf. on Atom ic Physics (Ann. Arbor) Abstracts px-12 (1990)
[15] H Pauly A tom ic and M o lecu la r  Beam s M ethods  (eds) G Scoles. D Bassi, U Buck and D Laine (Lx>ndon : Oxford University Press) p ^  
(1988)
[19] W Fritsch (private communication) (1988)
[21] K B MacAdam (to be published) (1991)
[23] T Roy P hD  Thesis (Uni /ersity of Cal.^ J va, India) (1992)
(Xl)
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Notes fo r  Contributors 317
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Our Special Publications

Ganguly, Nandita D

Iyer, K N

;,„/»<«./ /’/'V'- 8® 335-339 (2006 ) V A e v i e w
U P
Impacts of the 20*** January 2005 solar proton event on the ozone
concentration of Indian cities
Nanclitii D Cj;|nguly and K N lyei '
' Depai-lnic'nt of Physics. St Xa\ict'jf rollciic, Ahmcd.ibad-.IHO OOb, tJuiaial. India 
M.)cpartmciil of Physics. Sauiasht  ^ IJnivcisiiy. Ka)kot-"s60 OO.*). Cki|aial, India
P—mail HanditatlC«'icciicl nci
R t u ( ' i v c ( f  / D i ‘i rm/f< r  0 ( t c p i a i  2 7  h ( ‘h n ic i}\  2 n o o
\l)stract The o/onc data obtained fiom Nimbus ? and liailh piolie 'Idlal O/one Mapping Speciiomclei (TOMS) has been used to study the
cl coional mass election (C'MK) on the eolumnai o/one concentiation in India A compaiison of \.o>nmnai o/one values loi dilfctent solai 
piaioii c\cms (SPF) obseivcd at Srinagar mdiea’lcs that although the 20"' J.in . 2005 SPP, was the most intense in the last 15 years, the o/one depletion 
I Him! to he maximum in the 23'" Maich, 1001 event loliowed by 20"' Jan , 2005, 4"' No\ , 2001. 10"' Oct . 1080 anil 28"’ Oct , 2003 events .A 
,>mp )i!sv)n I'ctween the o/one levels obseivcd in dilleicnt Indian cities loi a lew days attei tlie 20"' Ian . 2005 SPH indicates that the o/one values were 
!.iiHul to (leitcase sharply at higher latitudes compared to places loeateii in the tropics 3'hc o/oiic values mcasuied by 3'OMS. Dobson Spectioinclci 
.iiid m :R\ O/onc Monitoring Instrument (OMI) wcic lound to ilcireasc loi a short pciiod tiom 20'" Jaiiuaiy to 25"' Janiiaiy aftci vihich the o/one 
ini-U ^^ allld letovciing to no'mal values The veilical o/one piotlles obtained fioin Miciowave lamb Somulei loi New Delhi, indicate that the o/one- 
mi\ine iatu> m the 3 0 to lOO hP^piessure range deeicased consistently fiom 2 I'' Jan , 2005 to 25"' Jan , 2005 and iheieaftei, reeoveied by the 3 I ' 
i,m ihii\. 200S
Kci words ■ (>/onc depletion. M>lai pioton evenl (.SPP,), ei^ ional mass ejection (r*MB), HO , NO^  
hV( S Nos. 06 60 Wh; 06 60 Kd, Ot 30 Db
1. Introduction
I aiTo solar storms rain electrically charged particles called 
pioions down on Barth’s atmosphere, which break up molecules 
nt gases hkc nitrogen and water vapt)ur, and once freed, these 
iionts teacl with ozone molecules and deplete the uppcrdevel 
'^7one lor weeks to months thercafterf 1 ]. The enhanced ionization 
''Elects not only the ionosphere but also some o f the minor 
neutial constituents between upper stratosphere and the 
' e^.sopausc. Odd hydrogen (HO^ = H+ O H + H O J  and odd 
.species (NO^ = N+NO+NO^) are produced by proton 
i^nd secondary electron impact on N,,. When nitrogen gas 
'^ t’lccules split apart, they create molecules, called nitrogen 
which last several weeks to months depending on where 
ihey end up in the atmosphere. Once formed, the nitrogen oxides 
’tact quickly with ozone and reduce its amounts. When 
‘‘imuspheric winds blow them down into the middle stratosphere.
they 3^in stay there for months, and continue to keep ozone at a
’educed level. Protons similarly affect water vapour molecules
Corfcsponihng Author
by breaking them up into lot ms where they react with o/.tme. 
However, these mt)Jecules. called hydrogen oxides, last only 
during the lime period o f the solar proton event. I'he.se short­
term effects ot hydrogen oxides can destroy up to 70 percent c^ f 
the ozone in the middle mesosphere. At the same time, long­
term ozone loss caused by nitrogen oxides destroys a maximum 
o f about nine percent o f the ozone in the upper stratosphere|21, 
Jackman e/ a l  f3| used their two-dimensional chemistry and 
transport atmos)>heric model to .simulate the influence o f solar 
proton events (SPBs) over the 1965 to 1995 time period. They 
found that extremely large particle events with huge fluxes of 
very high-energy protons occurred in August 1972 and October 
1989 and caused large increases in long-lived NO^ constituents, 
which affected t^zonc for several months to years past the events. 
The SPIi-produced NO^ constituents in the upper stratosphere 
caused direct ozone losses. They predicted a seasonal 
dependence ft^ r the impact on polar ozone, with larger (smaller) 
decreases predicted for ,SPEs occurring in the fall or winter 
(spring or summer). Verronen c f  a !  [4] studied ozone depletion
© 2 0 0 6  lA C S
336 N cuuhU i D  G an i> iJy  a n d  K  N  Iy e r
in  the no rthern  hem isphere  m id d le  a tm osphere  due lo  the 
O ctober-N ovem ber, 2003 solar p i\)ton  events. They (^b.served 
an increase in N O , concen tra tion  by several hundred percent 
and a s im ultaneous decrease in ozone by tens o f  percent at 
a ltitudes above 36 km. I he m ax im um  effect, a 60%  reduction in 
oz(^ne at 42 km , was ob.scrved in the end o f  N ovem ber, a m onth 
a fte r the solar proton event. A fte rw a rd s , a pa rtia l recovery o f  
ozone occurred towards the end o f  the year. Jackm an et al  [5 ] 
studied the im pact o f  solar storm s in O ctobe r—N ovem ber, 2003 
on the m idd le  atm osphci ic po la r cap icg ions .
1'hcy ob.scrved that the h ig h ly  energetic protons associated 
w ith  the wSPlis produced io n iza tions , exc ita tions , d isstK 'ia tions, 
and d issocia tive  ion iza tions  o f  the background constituen ts, 
w h ich  led to the production ot'odd hydrogen (H O  ) and odd 
nitrogen (NO^) w h ich  was observed by the U A R S  /  I IA l.O H  
instrum ent to increase ove r 20 ppbv th roughou t the southern 
hemisphere p ida r lo w e r mesosphere. I 'h e  N O A A  16 S B lJV /2  
instrum ent measured a short-te rm  ozone dep le tion  oi 'AOVc  in the 
sou thern  hem isphere  p o la r lo w e r m esosphere , w h ic h  was 
p robab ly due to an increase in IJO^. S B U V  /  2 observations 
showed ozone dep le tion  o f  about 5—8% in the .southern po la r 
upper stratosphere lasting  fo r  days beyond the event, w h ich  
was attributed to enhancement in NO^. The Goddard Space F lig h t 
C^entcr tw o-d im ens iona l m odel p red ic ted long -te rm  northern 
hem isphere po la r tota l ozone decrease greater than 0 . 5 to last 
fo r over 8 months past the events. T hey concluded that although 
the p ro d u c tio n  o f  NO^ c o n s t itu e n ts  is the  sam e in  bo th  
hemispheres, the NO^ constituents have a m uch la rger im pact in 
the northern than the southern po la r la titudes because o1 the 
seasonal d iffe rences between the tw o  hem ispheres. Between 
January 15*‘’ and 19^'\ 2(X)5, fo u r p o w e rfu l so lar flares erupted 
from  sunspot 720. Then on January 20, the f if th  exp los ion  
produced a coronal mass ejection (C M E ) that achieved veli>cities 
in co m p a ra b ly  greater than a n y th in g  astronom ers had seen 
before. W h ile  it gene ra lly  takes m ore than 24 hours ft)i* the 
charged partic les o f  a so lar ou tburst to  reach the earth, th is  one 
was a profound exception. Just th ir ty  m inutes a fte r the exp losion. 
Earth (some 96 m illio n  m iles away from  the sun) was immersed in 
what N A S A  scientists ca lled  the m ost intense p ro ton storm  in 
decades. The solar energetic pa rtic le  event o f  January 20, 2005 
has been the most intense in  15 years, w ith  a greater than 100 
M e V  pro ton in tens ity  com parab le  to that o f  the O ctober, 1989 
event [6 -8 ] .This event was also the largest g round-leve l neutron 
m o n ito r event in m any years, p ro v id in g  ev idence that protons 
were accelerated to energies o f  several G eV  [9 |.
2. Data and analysis
The ozone data obta ined fro m  N im b u s -7  and E arth  probe T ota l 
Ozone M apping Spectrom eter (T O M S ) fo r  the years 1989 -2(X)5 
has been used to study the im p ac t o f  C M E  on the co lum n a r 
ozone in  Ind ia . T O M S  is a source o f  h igh -re s (4u tion  g loba l 
in fo rm a tio n  about the to ta l ozone con ten t o f  the atm osphere. I t
measures the u ltra v io le t sun ligh t back scattered from  ihr l^ou ] 
o r  the ground to  measure the to ta l ozone am ount.
The va ria tio n  in co lu m n a r ozone values detei hum
sate llite -based T O M S  data is suppm ted  w ith  grenmd 
ozone data m easured w ith  D obson S pectrom eter at Delhi H,. 
D obson Spectrom eter is w id e ly  used fo r measuring iht ip, ,| 
co lum n a r ozone con ten t in the atm osphere. It u.se.s ihc 
since ozone has a series o f  hands in the u ltra v io lc i 
spectrum, by m easuring the solar u ltra v io le t radiation tiansmnmj 
to  the surface al several pa irs o f  w ave leng th 's , one c l*)sc ru .u 
ab.sorption m axim a, and one aw ay fro m  it, the total atlmup.,, 
ozone content can be ca lcu la ted.
The total co lum nar ozone values obtained from  A l !R \  ( )/oiu' 
M o n ito r in g  In s tru m e n t ( ( J M I)  and v e rtic a l ozone piulih^ 
m easured by M ic ro w a v e  L im b  S ounder (M L S ) ha\c been 
obtained through G E S -D IS C  Interactive O nline Visuali/aimn .md 
A na lys is  In fras truc tu re  (G io v a n n i).
Ozeme M o n ito r in g  Ins trum ent (O M l)  m on ito is  the lee \ci\ 
o f  the s tra tospheric  ozone layer. It measures both uitMMuki 
and v is ib le  ra d ia tion  and prov ides d a ily  h igh -rcso liu ion  gluh,; 
maps and p ro file s  o f  c^zone. M L S  is a m icrow  avc scnsoi, whi Ji 
is able lo  measure trace gases ins ide the clouds. It locust s un 
the upper troposphere and stratosphere, measuring niKiownxt 
radiatit^n em itted by ozone, ch lo rin e  com pounds and m.iriv uilu', 
traces gases.
3. Results and discussion
A  com parison o l'c o lu m n a r ozone ob ta ined from  N im hiis 7 .md 
E arth - probe 'TO M S  fo r  three to  s ix consecu tive clays .iitci 
d iffe ren t SPE events ob.served at Srinagar (34 N, 74.8 F.) is sru)y\n 
in F^'igurel.It is observed that a lthough  the 20"' Jan., 20(1"^  M’l
Figure 1. C^ omparison of columnar ozone for three to six con 
days in different SPE’.s observed al Srinagar.
Im pacts o f  the 2 0 th  Ja n u a ry  2 0 0 5  so la r  proton event etc 337
(he intense in the last 15 years, with >100 M eV prou^i 
intensity comparable to that o f the October, 1989 event, the 
,7one depletion was found to be maximum in the 23'^ * March, 
‘,« 1  event followed by 20“' Jan.. 2005,4“' Nov .,2001,19“’ Oct., 
H)S9 and 28’‘* Oct., 2003 events. This may be because a volcanic 
u p tu rn  Hekla was reported in Iceland on the 17*''January, 1991. 
The eruption cloud was north o f the terminator in the polar 
nit-h! region for the first few days o f atmospheric residence, s|nd 
then )l moved south across Russia and was detected by TOMS 
neai the Black Sea. Volcanic eruptions are potential sourceS.of 
 ^ BrO and l U O  in the lower stratosphere. SO, emitted 
liom the volcanoes gets converted into H., SO^ and condenles 
into small aerosol particles in the stratosphere. These aerosol 
;l(Hids piovide an increased scope for hctcrophasc chcmiijtry 
iindenhanced ozone depiction. Volcanic particles generally tike  
two (M three years to settle out o f the stratosphere. The large 
dcplciinn in ozone levels ob.served after the 23“* March, 1991 
.SPii may be due to the combined effects o f the Hekla volcanic 
01 upturn in Iceland and SPE.
A compari.son o f ozone values for different Indian cities 
ulici the 20"' January, 2005 SPE indicated that the ob.served 
dcnea.se m ozone values was found to vary with latitude. J’he 
o/onc values were found to decrease sharply at places situated 
ai highei latitudes like Srinagar and Delhi (First solid line and 
liisi dfjiiecl line respectively in Figure 2) compared to places 
iocaletl in iHc tropics like Rajkot,Trivandrum and Hyderabad 
(^ cc(Mid. thud and fourth solid lines respectively in F'igure 2).
1 his is liccause .solar storms lead to ejection o f large amount o f 
lii^h cnergy protons that can penetrate the Earth's magnetic 
lidd near the poles. These protons penetrate into the atmosphere, 
(40 to 80 km layer) causing ionization o f air molecules. As the 
loni/.cd jiarticlcs recombine, they produce nitrogen and hydrogen
Srinagar (34N, 74 8E) 
Rajkot (22 3 N. 70.8 E) 
Tiivandium (8 5 N, 77E)
Delhi (28 5 N. 77 3 E) 
Hyderabad (17 5N, 78 5E)
oxides, which can affect ozone through the NO^ and HO^ catalytic 
cycles.
The decrease in ozone values using TOMS data was 
observed for a shcjrt period from 20"’ January to 25"’ January 
after which the ozone levels slatted recovering to normal values 
(Figure 2). .Similar results were ob.served for ground based 
columnar ozone values measured with Dobson spectrometer at 
Delhi from 19"’ January to 28"' January (Figure 3). These effects 
are short-lived because the hydrogen oxides which cause the 
primary ozone loss recombine within hours.
3 3 0
Day of January 2005
F igure 3. ('o luinnai o /onc iccoidecl at Delhi iisiny Dobson Spcclioim  tcr 
fiom  19th lo 2Sth Januaiy. 2005
An examination o f total columnar ozone values obtained 
from AURA Ozone Monitoring In.strument (OM I) indicates that 
the ozone levels in northern and central India on the 24"'/25"* 
January, 2005 were lower by about 20 to 30 Dobson units 
compared lo 20"‘ /2 1''* January, 2005. fhe ozone levels therealter 
started recovering gradually around the 30"'/31'*' January, 2005 
(Figure 4).The recovery in ozone levels was ob.served to be 
faster in northern India, compared to central India.
. 20/21 Jan , 2005 
• 30/31 Jan , 2005
- 24/25 Jan , 2005
t* 2 r' 1
uiiiH r ozone measured by TO M S  over different Indian
20th lo  31st January, 2005.
Latitude
F ig u re  4. ro lu m n a i o /onc values fo r Indian latitudes obtained from  
AURA Ozone M onito ring Insirumenl for Jan., 2005.
NO is the most important destroyer o f ozt>ne in the 25*45 km 
altitude region. In the NO^ cycle, the radical that destroys ozone 
is NO.
338 Nandita D Ganguly and K N Iyer
I 'h e  ca ta ly tic  cyc le  is;
NO  + O NO  , + O^
NO^ + O NO  + O ,
NET: 0 , +  0~~>20^.
T h is  process is ca ta ly tic  since N O  in itia tes  ozone destruction 
process, but is regenerated, so that no net consum ption  o f  N O  
(K'curs. In the hydrogen cyc le , the rad ica l w h ich  destroys ozone, 
is the H yd roxy l radical O H .
The catalytic reaction is:
0 / 7  + 0 ^ —> HO.  + O .
HO.  4- O -  > OH  + O y  
NET: 0^ + 0 - ^  2 0 .
Other members o f  the I lO.^ fa m ily  w h ich  destroy ozone arc H 
and HO  ^
7/ + O , OH  + Oy 
OH + O ~>H + Oy  
NET: O , 4- O —>20y
HOy>tO -> O H  ^  Oy  
0 H ^ 0 , - - > H 0 , +  0 . .
NET: O j  + O ~> 2 0 .
A n  exam ination  o f  ve rtica l ozone p ro file s  ob ta ined from  
M ic ro w a v e  L im b  Sounder fro m  -  3 Jan., 2005 fo r  N ew  
D e lh i (F igure 5) indicates that the ozone m ix in g  ra tio  m ppm v in 
the 7.0 to 3.0 hPa pressure range (a p p ro x im a te ly  32 to  40 km  
a ltitude  range) is found to decrease con s is ten tly  fro m  21'’  ^Jan., 
2005 to 25 ‘^^ Jan., 2005. The ozone levels are found  to  recover by 
the 31''^ o f  January, 20(J5. The S PH-produced NO^ constituen ts 
in the upper stratosphere cause d irec t ozone losses. H ow ever,
12 ,
20 22 24 26
Days Of January 2005
28 30
interference o f the NO^ constituents with the halogen h^ ss eycl 
for ozone destruction might have actually led to .some o/.ori 
production in the 15 to 25 hPa pressure range (approximatcK 
to29 km altitude range) on the 25*‘’ and 26^ January. Jackman m 
al [3J observed similar results in their two-dimensional chemist^  
and transport atmospheric model. Since the solar proun; ; 
is found to deplete very little total ozone for a short pcnod -n 
India, its negative impacts on humans will be very little
4. Conclusions
Ozone data obtained from Nimbus- 7 and Earth- probe I OMs 
for the years 1989 - 2005 has been used to study the iinj\ui o| 
CME on the columnar ozone in India. A comparison ol cuiumnai 
ozone for different SPH observed at Srinagar indm.iics ih.n 
although the 20‘*^ Jan., 2005 SPH event was the most ihkhvc m 
the last 15 years, the (V.one depletion was found to be iruMirium 
in the 23'^  ^March, 1991 event followed by 20^ *^  Jan , 2005. 4"‘ 
Nov., 2001, 19‘“ Oct., 1989 and 28^ '* Oct., 2()(J3 ewnis I he 
observed decrease in ozone values during the SPI- w.m jouini 
to vary with latitude. The ozone values were found to dc(hmsc 
sharply at higher latitudes compared to places located m ihc 
tropics. The decrease m ozone values was observed Im a sIkw- 
period o f about 5 days, after which the iizone lc\cK siaitcJ 
recovering to normal values.
Acknowledgments
The authors wish to acknowledge their gratitude to Piol .Mn i'v. 
Lai, r^iysical Re.scarch Laboratory, Ahmedabad and Di S \hm.ki 
N ASA  Goddard Space Flight Center for valuable sugpcMi Hi. 
and discussions. Dr Sunil Peshin, IMD, Delhi, for pun idin - ih; 
Dobson Spectrometer data at Delhi and the Ozone Pmccssiiiii 
Team o f the Atmospheric Chemistry &  Dynamics B m i u I i .ti 
Goddard Space Plight Center, for the production and disti ibuiion 
o f TOMS ozone data. Figure 4 depicting the distributu'n  ^l 
columnar ozone at different Indian latitudes and vcrtic.i' 0, 
profiles (Figure 5) used in this study, were acquired usmr ih; 
GHS-DISC Interactive Online Visualization and A h.iIvm^ 
1 nfrastructure (Giovanni).
References
I 1 ] http.//w\v\\\ciin. voni/nc\vs/cnn-storuw/200! 
storms ,44529.asp
[2] Chandler Lynn htlp;//svww gsfc.nasa gov/io|>si'H'
200l080Isoiarprotun.html (Aug 2001) 
t.lj C H Jackman, E L Fleming. P M Vitt anti D B ( onMcImc 
Spare Res. 24 625 (1999)
f4] P T Verronen, A ScpplitU. L Backman. E Kyi Ola. S
J Rodger. M A Clilverd, A Hauchecome, J L Bertaux, i> ‘
F Hnell, E Turunen and T H Ulich C A L  M id te r m  K e v u w  
(E lo u n d a ,  C r e t e .  G r e e c e )  (2005)
Figure 5. Vertical ozone profile.^  for New Delhi obtained from Microwave 
Limb Sounder from 2(y*‘ - 3P' Jan., 2005 .
t5] CM Jackman, M T Dcland, G J Labow, E L Flctni 
Wcisenstcin, K W K Malcolm, M Sinnhuber, M Janies
n-. 
anU ■'
Impacts o f the 20th January 2005 solar proton event etc 339
K IIS sc I ./, Gvophys. Res. 110 A09S27 doi: 10 1029/
.()041A010888 (2005)
A Mcwaldt. M P Loopcr, C M Cohen, G M Mason, M 1 Desai. 
D K Haggc’rty. A W Labrador. R A Lcske. J E Ma/ur, E (' Stone. 
Volt Rosenvinge and M B Wiedenbeck . Aineiican (ieophxsiral 
Sprinif Meeting 2005. abstract #SH32A-05 (2005)
\  W Labrador, C M Cohen, R A Leske, R A Mcwaldt, B C Stone, 
fvj 1- Wiodenbeck.Ci M Mason, M 1 Dcsai, Von Rosenvinge. M D
Loopei, J E M a/ui, R S Selesnick and I) K Haggerty. American 
GeopUssun! Ihunn, Spnn\’ Meeting, 2005. abstract #SH33A*04  
(2005)
18] A Seppalii, P T  Venonen, M A ('lilvcid, (' J Rodger, E Tiiiimen. 
Th Ulich and ( ’ E Enell lAGA Confemue Pwc. 2005, (Toulouse, 
home) (2005)
19] E 0  Eluecktger, R Huclikoler, M R Mosci and L  Desorghci Imp f 
/\v\\'w\a i^oo( cnmn t onferent c o/*g (2005)


Impacts of the 20th January 2005 Solar Proton Event on the Ozone Concentration of Indian Cities

Acharya, Anjana

jnJinn J. Phys. 8 0  ( 4 ) ,  4 0 9 - 4 1  1 ( 2 0 0 6 ) ote
Complex shape parameter for .v-wave scattering from zero-energy wave functions
A n jR n a A c h u ry a
I^ c p a ilm c n t o f  Phys ics . 4 j iu v c is i iy  C 'o lloge tiC E in g in cc iin g , 
B u ila -7 6K  01 S am ba lpm .O nssa . Ind ia
B -m a il |anjanaC«)K)ph ic s . in
Ret c iv r c l / y  iJt'f 200^, t ir i  cptci/  7 f ’ch n u u 'x  200ft
\ l)s t ra c l . U s ing  an cxlc*nsion o l ih c  m ethod o l K erm ode and Van I>i]k. ( /V/v.v Rev <M2 1S91 (1990 ) ] \vc show  how  a c i>m p lc \ shape pa iam eter 
lot c(’>mplev lo ca l p o te n tia l can he d c te i m ined  in ic im s  o f  /e io -e n c ig y  wave Inn c tio ns  fo r  \ -wave sca ttenng
Keyw o rds E lT e c liv c  la ng e  the o ry , shape p a ia in e te i. /e io -e n e ig y  wave fim e tio n s
PV(’S Nos. 21 10 .-k .2 1  9 0  + r
It has re c e n tly  b e e n  s h o w n  th a t  th e  s h a p e  p a r a m e te r  ( P )  a n d  c o - 
d tic ie n ts  o f  h ig h e r  p o w e r s  o f  in  th e  e f fe c tiv e  ra n g e  e x p a n s io n  
(P.RI: ) fu n e tk ^ n s  m a y  b e  o b t a in e d  fro m  th e  z e r o - e n e r g y  w a v e  
tiinctions fo r  a re a l lo c a l p o te n tia l  w h ic h  s u p p o r ts  n o  m o re  th a n  
one b o u n d  s ta tc [  I ]. T h e  u s e f u ln e s s  o f  th is  a p p r o a c h  lie s  in  th e  
lact that c a lc u la tio n  o f f *  is n o t g e n e r a lly  s im p le  i f  th e  p o te n tia l  
IS nt)t o f  a s im p le  f o rm  a n d  th e  s h a p e  p a r a m e te r  is s m a ll  in 
m agnitude.
In th is  n o te , w e  e x te n d  th e  a p p r o a c h  o f  K e r m o d e  a n d  V an 
n i j k |2 | fo r  c o m p le x  lo c a l p o te n t ia ls  a n d  tr y  to  s e e  w h e th e r  th e  
shape p a r a m e t e r  in  s u c h  a s i t u a t i o n  c a n  a ls o  b e  o b ta in e d  
reasonably s im p ly  to  p e r m it  its  a p p lic a t io n  to  a n tip r o to n -p r o to n  
scatterings. H e n c e , w e  h a v e  d e r iv e d  a n  e x p r e s s io n  f o r  c o m p le x  
shape p a r a m e te r  in te r m s  o f  i n te g r a ls  o f  th e  z e r o - e n e r g y  w a v e  
tu n clio n s.
In v ie w  o f  th e  p r e s e n t  e x p e r im e n ta l  w o r k s  w ith  lo w  e n e r g y  
iin tip ro to n s s c a t t e r i n g  o f f  p r o t o n s  b o t h  e l a s t i c a l l y  a n d  via 
^annihilation c h a n n e l ,  th e  d e t e r m i n a t i o n  o f  e f f e c t i v e  r a n g e  
param eters h a s  b e e n  o f  c o n s i d e r a b le  i n te r e s t  I 3 - 6 ] .  K ro ll  a n d  
Schw eiger [ 7 |  h a v e  f o u n d  a  s e t  o f  c o m p le x  s q u a r e  w e ll p o te n tia l  
param eters fo r  v a rio u s  p a rtia l  w a v e s  w h ic h  s e e m  to  fit th e  a n g u la r  
d is trib u tio n s a n d  th e  p  p a r a m e t e r  r e a s o n a b l y  s a t is f a c to r i ly , 
fliey u se  d i f f e r e n t  r a n g e s  f o r  re a l  a n d  im a g in a r y  p a r ts  o f  th e  
potential in  th e  prCvSence o f  c o u lo m b  i n te r a c t io n .
W h ile  K ro ll  a n d  S c h w e i g e r  u s e d  d i f f e r e n t  r a n g e s  f o r  re al 
iind im a g in a ry  p a r ts  o f  th e  s q u a r e  w e ll  p o te n tia l  f o r  r e a lis t ic  d a ta
fittin g  , w e  h a v e  s im p lif ie d  th e  p ro b le m  by ta k in g  id en tica l ra n g e s  
fo r  b o th , s in c e  at th is  s ta g e , o u r  in te n tio n  is o n ly  to  d e m o n s tr a te  
th e  u s e f u ln e s s  o f  th is  m e th o d  a n d  n o  c la im  is m a d e  a b o u t th e  
a c tu a l d e te r m in a tio n  o f  s h a p e  p a r a m e te r  fo r  a n tip ro to n -  p ix n o n  
s c a tte r in g . W e w o u ld  n e e d  to  in c lu d e  c o u lo m b  m o d if ic a tio n  in 
th is  a p p r o a c h . A t th is  s ta g e  o f  a v a ila b le  in f o r m a tio n , it w ill b e  
p r e m a tu r e  to  la y  a n y  c la im  to  th a t e ffe c t s in c e  e v e n  s c a tte r in g  
le n g th s  a n d  e f f e c t i v e  r a n g e s  a r c  s till  to  b e  u n a m b ig u o u s ly  
id e n tif ie d . In v ie w  t^f th is , fo r  d e m o n s tia tio n  p u r p o s e s , w e  h a v e  
u s e d  p o te n tia l  p a r a m e te r s  w ith  id e n tic a l ra n g e s . W e th u s  s h o w  
th a t K e r m o d e  a n d  V an  D i j k ’s a p p r o a c h  c a n  b e  e x te n d e d  to  
c o m p le x  p o te n tia ls  a ls o  w ith  s o m e  m o d ilic a tio n s .
Com plex shape param eiet :
H e r e , w e  h a v e  ta k e n  a s p h e r ic a lly  s y m m e tr ic  lo c a l c o m p le x  
p o te n tia l ( V (/) 4- iW {r ))  in s te a d  o f  a  real p o te n tia l. W e d e f in e  th e  
re a l a n d  im a g in a ry  p a rts  o f  th e  .v-state w a v e  fu n c tio n s  a s  (////  ) + 
i a y ) )  f o r  e n e r g y  k - a n d  f o r  z e r o  e n e r g y
re s p e c tiv e ly  a n d  a s s u m e  th e  s a m e  b o u n d a r y  c o n d itio n s  as g iv e n  
b y  K e rm o d e  a n d  V an D ijk  fo r  b o th  re al a n d  im a g in a r y  p a r ts  
s e p a ra te ly  i /c.
/, ( 0 )  =: = « ( 0 )  = / / „ / 0 )  = 0 ,  ( l a )
u ,(R )  =  « „ ,(/ ? ) .« ,(/ ? )  =  « ,„ (/? ). ( l b )
u ,(0 ) =  « „ / 0 )  =  1, « , ( 0 )  =  « o ,(0 )  =  0 ,  ( lc>
© 2 (X X iIA C S
410 A njana Acharya
w h e r e  R  is th e  d is ta n c e  b e y o n d  w h ic h  b o th  re a l a n d  im a g in a r y  
p a r ts  o f  th e  p o te n tia l  a re  n e g lig ib le . A s  m e n tio n e d  a b o v e , w e  
a re  a s s u m in g  f o r  c o n v e n ie n c e , th a t  R  is id e n tic a l  in b o th  c a s e s . 
D e f in in g  a c o m p le x  s h a p e  p a r a m e te r  P  =  P  +  iP  ^ in th e  s ta n d a r d  
e f fe c tiv e  ra n g e  e x p a n s io n  fo r  th e  c o m p le x  p o te n tia l .
w ith
K  c o t {Sr +  iS,) =  "  \ /  {a,. + ia , ) + 1/2  + />o, )k  *
- { P ,  + i P i ) { 'a ,  +//•(,, (2)
t7^(r)= 1-|/-«,./ («; +«,?)} + r/(,r<:‘ /2 
+  ^ k - r ^ a , l { f j { a ;  +  k ' l - - / l ,  ,
//,.( r )  =  | r  < 7 ,/ ( « ;  +  a f  ) }  +  r r ^ i k - / 2  +  { ^ j b [ a f .  +  a ' )]
w ith  ^ '\s  a s p h a s e  s h if ts , a ’s a s  s c a tte r in g  le n g th s  a n d  a s  
e f fe c tiv e  ra n g e s . It c a n  b e  s h o w n  th a t  P  s a t is f ie s
( P, + iP, )  (/•„,. +  ;/j,, y ' k - - k - * { ........ )  =  +  (•/<„, )■
- (" r  + i" i ) («or + '"o;) -  (“0/ + iiiQi) '  + (“r + '“i ) (“o/- + '■''o,)] (if
(3 )
a n d  h e n c e  in  th e  lim it —> 0 ,w e  <.)btain e x p r e s s io n s  fo r  P^ a n d
P  ^ in  te rm s  o f  z e r o - e n e r g y  w a v e  f u n c tio n s  a s  f o l lo w s
( +  if", ) in)r +  i 'b , f  =  ''T l*  2 - .0  > / +  '« 0 , ) ’
(“0/ + '“o<)-("()-- +'«<»/)' + (“i- + '» , ) (“()/•
(4)
H o w e v e r , th e  a b o v e  e x p r e s s io n s  s till  c o n ta in  ii^ , a n d  ii^ 
w h ic h  a rc  n o t z e r o - e n e r g y  o b je c ts . In  o r d e r  to  g e t r id  o f  th e m , 
w e  d o  a  T a y lo r  e x p a n s io n  in  k^ a n d  w rite  th e  w a v e  fu n c tio n s  in 
te rm s  o f  c o m p le x  o b je c ts  (3  ^ +//?, a n d  + Pi
u, (r) + iUj(r) = Jj + (r) + //?, (/))*  '  (r) + /«(,, (/•))] (5 a)
(i7r(r) + /«;(r)) = |l + (/9^  +/?)A:-J(/7o,(r) + H7o,(/■))]. (5b)
T h is  le a d s  to
(P r+ iP ,)(ro ^+ ir(h f
=  +  'A ) ( " O r  +  " 'O i ) "  “  (Ar +A ,)  ( “ o r  +  '" O l ) " ]  ( 6 )
w h ic h  a f te r  s e p a r a t io n , g iv e s  th e  r e a l  a n d  im a g in a r y  v a lu e s  o f  
th e  s h a p e  p a r a m e te r .
However, (P^ + ) ^nd (P^ + /P ) are still to be determined.
Determ ination o f  functions p { r )  and P { r )  *
Since we have,
{Jif (r) -f- iw/ (r ))  = sin(A:r) cot (S^ + iS i) + cos(^r)
(7h,
to  o r d e r  o f  k ~ , a n d  it  ^ \s  b e in g  th e  f o l lo w in g
'■'0r('-) = ! - { ' •  ( I r / { c r  + «/‘  ) }  , (Ku
«0. ('•) = {'■ ^'//(«," + o f  ) }  . (M.i
U s in g  e q u a t io n s  ( 5 ) , ( 7 )  a n d  ( 8 ) ,  w e  o b ta in
Ar (f") =  '  [{ 3 (« f  -  of - '■  ) ('b , -  '■ ) + ( " ,  -  '■ ) + 3/- j j
6 ( ( « , . - r ) ' , ,1).,,
A, ('•) = '|{3/b, { ‘ i f  + d f  -  r  Hr ) + 2 r-a , -  3/- a,i„,  ^ !
+ « , ' ) j  . (%i
T h e s e  a p p e a r  to  b e  c o r r e c t  e x p r e s s i o n s  b e c a u s e  / / (/  
r e d u c e s  to  K e r m o d e - V a n  D ijk 's  P ^ ir )  w h e n  im a g in a ry  part is 
s w itc h e d  o f f  w h ile  p j { r )  b e c o m e s  z e r o  u n d e r  th a t condition 
P r^ r)  a n d  P ,{ r )  c a n  n o w  b e  d e t e r m i n e d  b y  su b stiu itin y  
( )  fro m  e q  (."S) in to  th e  a p p r o p r ia te  S c h r d d in g e r  equation
g iv in g
{A r + i p  )" ( " O r  + '"0/ ) + 2(/?,. + i p  )'• («0r + <"(), )"
+(• +(A - ("Or + '"o;) = 0. (lOl
L e tt in g  > 0 ,  w e  g e t a  d if f e r e n tia l  e q u a tio n  fo r  c o m p le x  p '  
a s
("or + '«0/f (A- +'V5j)'= -(«or +'«0/)'
r
=  -  J  ("o» (-^) + '" o . .
The constant of integration is taken to be zero 
convenience.
Complex shape parameter for s-wave scattering from zero-energy wave functions 411
f\pplication to complex sc/uarc-well potential o f identical expressed in terms of the zero energy wave function. This feature
is especially useful in the determination of the complex shape
i hc appropriate informations for a com plex square-well potential Parameter, which is calculated i n a straightforward manner by
The 
ot depth
K-=V+ iW and range R are,
K =  K + i K ^ ,
K  = ( V + (  W ’ -t-
Mih
integrating simple functions made up of the square of the zero- 
energy wave functions. We have thus shown that Kermode and 
Van Dijk method can be conveniently extended to complex local 
ptitentials as well and a complex shape parameter can be defined.
H„, (f) =  Ar sinCA: /^') c o sh (A '/)-  4, co.s(A',r)sinh(A-,/) |
I
»oi ('■) =  cos(A^/-) sinh(A,r) -  /\, sin(A,.f)cosh(A,r) •!
" O r (r )  =  I +« , ■ ) } ,
(1, = /? - [/f, tan ( /f, /?) (l -  tanh' ( /f, /^)) + /f, tanh(K, R) 
^ { \U im \K ,R ))y (K ;-^K ^ )( l  + \m h\K ,R )\;xn^K ,R )),
a, =[Af, tan(/r,/?)(l-tanh-(A;',/?))-A:,tanh(A',/?)
(I + tan-(A:,/?))y(/r,- -t- /:f )(l  +tanh-(/f,/?)tan-(A:,/?)).
With the squarc-wcll potential for which R is taken to be the 
langeoflhe potential, we used R = 2.02 fm and K = 0.9343 fm”* 
and we found P = -0 .0 4 0  and P = -0 .0 0 6 . The finiteness to Pr  I I
IS interesting because the imaginary part of the potential is very 
large. We show in Figure 1 the // - functions and we note that 
while the behaviour of and is very similar to that 
obtained for purely real case, Pj and P, show a distinctly 
diticrent behaviour including some oscillations. Further, their 
magnitude is an order less than P,. 's. Again, we have shown 
•hat the coefficients of the effective range expansion can all be
Figure 1. The real and imaginaiy pans of the P  and /y functions foi 
the complex square well potential
References
11 ] L S RcKlherg and R M Thaler hitrodm turn to ihv Quantum Uwory 
of SratU'nni> (New Yoik : Academic) (1%7)
121 M W  Kermode and W Van Dijk /V/v.s. Kev C42 1S91 (IWO)
[31 J Mahalanabic, H J Pirner and T A Shihata Nurl Pliys. A485 546
(1988)
[4] H J Pirnei, H Kervikov and J Mahalanabic Z Phys, A338 I I I
(1991)
[5] A V Lagu in Pliy\ir\ at U'ar with hnv Enci\{>v Anttproums (eds) ( ’ 
Amsler et al (New York . Hat wood) p25l (1988)
(6| BO Karvikov Nurl. Phys. (Pror. Suppl) B8 273 (1989)
[7] P Kroll and W Schweigei Niul Phys. A503 865 (1989)


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