Volume 2013 Issue No.4, Dt. 16 April 2013 Time: 19h 20m P.M.
Some Experimental Investigations on
Nuclear Quadrupole Resonance and Graviton
by
by
Professor Dr Kotcherlakota Lakshmi Narayana,
{Retd. Prof.of Physics, SU, Kolhapur} 17-11-10, Narasimha Ashram,
Official Colony, Maharanipeta.P.O. Visakhapatnam -530002,
Mobile No. 9491902867 & 9542717723
keywords: Graviton, NQR
ABSTRACT
An experimental investigation of Nuclear Quadrupole resonance Spectra has been made in some covalent organic compounds. Resonances are newly detected for the following three compounds (i) α-Chloralose, (ii) 2,3, dichloro-thio-napthene and (iii) 5-Chloro-Salicyclic acid. The experimental value of the resonance frequency for 5-Chloro-Salicycli-sacid is in agreement with that predicted from a plot of frequency Vs Hammet’s σ- value. The Figure of NQR given shows the split resonance in 2, 5 dichloro-nitro benzene observed in the present initial experiments to test the experimental set up.
Fig. A gives the NQR signal reproduced theoretically in the present work. The observed spectrum Fig.1 (theoretical estimate See also Fig A), Fig.3 and Fig.7 reported herein was adjusted to a polynomial fit of 8th order equation and the parameter values are explicitly given.
The association of Graviton of Spin-2 with the Quadrupole of the nucleus of Spin-2 leads to
2 x 2 = (0 + 2 + 4) + (1 + 3)
where we know from Clebsch-Gordan coefficients the states with even angular momentum are symmetric and states with odd are antisymmetric in the two particles (each of Spin-2) so that the coupling envisaged here explicitly obeys
<2 i="">= (-1)^(2+ 2ˆ - I) * <2 i="">
It is well known that topology excludes the possibility of any spherically symmetric source of gravitational radiation (usually with l=S=2 refer p.978 of “Gravitation” by Misner, Thorne and Wheeler 1973).
An object of my work is that the Graviton of Spin-2 and Quadrupole of Spin-2 of several nuclei in the observation of the Nuclear Quadrupole Resonance experiments intrinsically involve the coupling of Gravitons with the Nuclear Quadrupole Moments.
INTRODUCTION
The NQR signal analysis.
Fig. A gives NQR signal reproduced using the 8th order equation by the author on 16 April 2013.
This Fig. A also gives the original picture of the NQR spectrum of
2, 5 dichloro-nitro benzene.
A theoretical spectrum obtained by explicit analysis by using an 8th Order polynomial in Fig.1.
x = linspace (-8, 8); y = sinc(x); plot(x, y)
Sin (πx)/ (πx) = (1/ 2π) ∫ exp (iωx) dω
from (-π to π). sinc function has a value 1 when x is equal to zero otherwise the value of the function sin (πx)/ (πx).
Fig.1 Theoretical reproduction of observed
spectrum
The data listed below refers to the theoretical spectrum given in Fig.1.
S.No
|
X- Value
|
Y- Value
|
S.No.
|
X-Value
|
Y-Value
|
S.No.
|
X-Value
|
Y-Value
|
1
|
30
|
130
|
11
|
165
|
50
|
21
|
290
|
62
|
2
|
30
|
10
|
12
|
170
|
81
|
22
|
345
|
90
|
3
|
65
|
82
|
13
|
185
|
175
|
23
|
350
|
65
|
4
|
68
|
50
|
14
|
191
|
78
|
24
|
368
|
85
|
5
|
98
|
92
|
15
|
200
|
45
|
25
|
368
|
50
|
6
|
100
|
70
|
16
|
221
|
65
| |||
7
|
109
|
85
|
17
|
225
|
108
| |||
8
|
109
|
50
|
18
|
240
|
110
| |||
9
|
151
|
70
|
19
|
245
|
70
| |||
10
|
151
|
89
|
20
|
290
|
103
|
The present author has succeeded in adjusting the observed spectrum to an eight order polynomial expression and the corresponding parameter values are obtained listed below and reported herewith.
[4/17/2013 09:42 "/Graph2" (2456399)]
Polynomial Regression:
Y = A + B1*X + B2*X^2 + B3*X^3 + B4*X^4 + B5*X^5
+ B6*X^6 + B7*X^7 + B8*X^8
Parameter Value Error
------------------------------------------------------------
A 506.05621 1280.11624
B1 -33.34514 96.31995
B2 0.95136 2.70618
B3 -0.0137 30.03852
B4 1.12004E-04 3.1095E-04
B5 -5.37281E-07 1.4815E-06
B6 1.49842E-09 4.12007E-09
B7 -2.24496E-12 6.17553E-12
B8 1.39548E-15 3.85028E-15
------------------------------------------------------------
R-Square (COD) SD N P
------------------------------------------------------------
0.06807 38.06165 25 0.9952
Fig.2 the polynomial fit obtained with an 8th order equation of
the present work.
Fig.3 of page 167 imag_9733 gives the experimental set up.
Fig.4 of page 165 presents the voltage vibrator and
the filament voltage for the detector.
Fig.5 presents the details of the super regenerative circuit.
Fig.6 presents the details of Fig.4 and Fig.5 on one page.
Fig.7 is explicit NQR spectrum reported in my Thesis and
also in the J. Shivaji University page 109, 1966.
Pages 109 to 111 refer to the reported publication (made on request) in the Journal of Shivaji University, Kolhapur (first journal publication of that University in 1966) [1]. Pages 163 to page 196 refer to the data of the Ph. D Thesis of the present author in 1964 degree awarded in 1965 while the author was at University of Uppsala, Uppsala, Sweden.
page 163
Page 164
Page 169
Page 173
Page 174
Page 176
Page 177
Page 178
Page 179
Page 180
Page 181
Page 182
Page 183
Page 185
Page 190
Page 193
Page 196
page :109
Page 110
Page 111
Page 113
Graviton and Quadrupole Union
It is envisaged in this paper that the Nuclear Quadrupole associated with the Nuclei in the Nuclear Quadrupole Resonance experiments, so nicely initiated by Late Prof K R Rao D.Sc. (Madras) D.Sc.(London) at his research laboratories in Andhra University, interact with the Gravitons resulting in a spectrum of very enlarged spectral levels. The present work identifies the
“the association of Graviton of Spin-2 with the Quadrupole of the nucleus of Spin-2 leads to
“the association of Graviton of Spin-2 with the Quadrupole of the nucleus of Spin-2 leads to
2 x 2 = (0 + 2 + 4) + (1 + 3)
where we know from Clebsch-Gordan coefficients the states with even angular momentum are symmetric and states with odd antisymmetric in the two particles (of each of Spin-2) so that the coupling envisaged here explicitly obeys
<2 i="">= (-1)^(2+ 2ˆ - I) * <2 i="">.
It is well known that topology excludes the possibility of any spherically symmetric source of gravitational radiation (usually with l=S=2 refer p.978 of “Gravitation” by Misner, Thorne and Wheeler 1973 [2]).
An object of my work is that the Graviton of Spin-2 and Quadrupole of Spin-2 of several nuclei in the observation of the Nuclear Quadrupole Resonance experiments intrinsically involves the coupling of Gravitons with the Nuclear Quadrupole Moments.
An object of my work
This yields a variety of spectra involving the angular momentum values ranging from +4 to -4. The intermediate values of differing symmetries can easily be envisaged by the group theoretical methods. The simple concept of just two values of +4 and -4 for the joint Nuclear Quadrupole Resonance experiments and the Graviton happens to be the simplest conjecture of positive and negative orientations along an angular momentum vector. This is similar to projections of Spin +2 and -2 of a Graviton along a preferred axis.
The other values like +3, +2, +1, 0, -1, -2, -3 are just the projections dictated by the interactions of the Graviton with the Nuclear Quadrupole resonance experiments. The analysis differs considerably from the thoughts of K. T. Hecht (1964) [3] in his papers on Collective Models. Not only the experimental observations made to-date on the Nuclear Quadrupole Resonance and as well on the Gravitons need to be totally analyzed explicitly in my model for detailed work outs and presentations.
Excellent research work on NQR experiments was initiated by Late Prof. K. R. Rao D.Sc. (Madras) D.Sc. (London) when several students obtained their Ph. D degrees. A small note was published by Late Prof K. R. Rao on NQR in the C. S. I. R. meet to award the research grants at New Delhi. The present author was lucky to join the C. S. I.R scheme in 1961 at Physics Department, Andhra University, Waltair awarded by the said organization.
ACKNOWLEDGEMENT
The author is greatly indebted to Late Prof K. R. Rao, D.Sc. (Madras) D.Sc. (London) for his continuous zeal in promoting the outstanding research work at AU, Waltair covering the entire Electromagnetism Spectrum from Cosmic Rays to the Radio waves during the years of his unselfish and devoted research in several branches and exceptional devotion in care-taking the youngsters to achieve glory and comfortable positions at several institutions in India and abroad.
REFERENCES
[1]. K. L. Narayana, Journal of Shivaji University,
Page 109, Kolhapur, 1966
Page 109, Kolhapur, 1966
[2]. C. W. Misner, K. S. Thorne and J. A. Wheeler, book on “Gravitation”, W.H. Freeman and Company, San Francisco, 1973.
[3]. K. T. Hecht, Collective Models in “Selected Topics in Nuclear Spectroscopy”, compiled by B. J. Verhaar , North-Holland Publishing Company, Amsterdam,1964
List of Publications on Gravitation by the author KLN while at Shivaji University, Kolhapur 416004, India. (1966 to 2000)
3. K. L. Narayana, et al, “On the violation of an inherent symmetry principle of
Spin 2 particles”, Nuovo Cimento Serie, 11, Vol.33A, page 641-648, 21 Giugno, 1976.
8. K. L. Narayana, “ The Uranium Quadrupole Moment based on a dual
core fissionable model”, Current Science Vol.38, p.261, 1969.
9. . K. L. Narayana & S. B. Patil, ”a Physical model for two-particle baryon
resonance systems and a postulation of medium and low interactions”,
Indian Journal of Physics Vol.50, pages 993-1002, 1976, and
Ind. Sci. Cong. Waltair, 1976.
*10. K. L. Narayana, “On the unification of Gravitation and the Quantum Theory”,
Shivaji University, 1979 and
Invited talk presented at GRG 8th National Symposium at Bhavanagar, 1978.
*17. K. L. Narayana,”A new field quantization approach to Gravitation and
Bosonic gravitons of Spin 5/2”, Indian Science Congress, Hyderabad,
Physics Section,(Late Paper), 1979.
*18. K. L. Narayana,”Spin 5/2 Graviton-like particles and their relativistic motion in
a central force field”, 66th Sess.of Ind. Sci. Cong. Physics Section Paper No. 1978.
*19. K. L. Narayana,”Physical orthonormalization criteria for gravitation
spinor wave functions, chirality projections and hyper-number √1”,
66th Sess. of Ind. Sci. Cong. Hyderabad, Mathematics Section Paper No. 1978.
*20. K. L. Narayana, ”Non-compact Group (3,2) spectrum for Graviton of
Spin 5/2 under Bose-Einstein Statistics and symmetry aspects”, Albert Einstein
Centenary Symposium, Bose Institute of Physical Sciences, Calcutta, Dec.31st, 1979.
*21. K. L. Narayana, “Perangon Symmetry transformations, space-time structure of
a biological cell, Exchange Theory of Cellular adhesion and
Bio-Quantum Machine”, Albert Einstein Centenary Symposium,
Bose Institute of Physical Sciences, Calcutta, Dec.31st, March 1-4, 1979.
*23 K. L. Narayana and C. Santhamma, “On Nuclear Quadrupole Coupling Constants
of Chlorine Isotopes and Dipole Moment of Br79Cl35 molecules”,
Indian Journal of Physics, Vol.37, No.5, May 1963.
24. K. L. Narayana, “On Nuclear Quadrupole Resonance in TiCl2 and CrCl2
Crystals”, Journal of Chemical Physics, Vol.43, No.6, p.2916, 1965.
25. K. L. Narayana and V. Nagarajan,”On Nuclear Quadrupole Resonances of
certain covalent compounds”, Shivaji University Journal, Vol., No.1 and 2,
pages 109-113, 1967.
49. K. L. Narayana and B. P. Sabale,”On Molecular Quadrupole moments of N2 and O2”,
Shivaji University Journal, Vol.6, p.32, 1973.
[A gap of seven years from 1973 to 1980 when K. L. Narayana involved in the
production of Ph. D thesis of his students at Shivaji University, Kolhapur.
A break of the authors research on Gravity, and Gravitation etc.
But he taught the Gravity aspects as a part of his teachings for
M.Sc. Physics students at that university. Resumed later in 1980.]
76. Dr. K. L. Narayana,”On other Gravity Possibilities of Gravitation”, Vol.1, p.641,
Einstein Centenary Symposium, Nagpur University, Nagpur, Duhita Publishers,
Einstein Foundation, Nagpur, Eds. K. Kondo and T. M. Karade.
held on Feb.20th, 1980.
78. K. L. Narayana,”Charmed spin 5/2 graviton within a super-gravity formulation”,
67th Ind. Sci. Cong. Sess, Physics Section, Jadhvapur University, Calcutta,
Paper No.5, February 2nd, 1980.
*79. K. L. Narayana,”Behrrung Gauge approach and an Unified Model of Gravitation,
Electromagnetism and Strong interactions”, 67th Ind. Sci. Cong. Session,
Mathematics Section, Jadhavapur University, Calcutta, February 6th
Paper No. 1980.
88. K. L. Narayana, “Space Science analysis of the 19th November 1977 Indian
Penninsular Double Cyclone and their gravitational interaction and a model of
a helical cyclonic metric structure”, Physics Section, Paper No.89, the 68th Ind. Sci.
Cong. Session, Banaras Hindu University, Varanasi, 3-8th January 1981.
89. K. L. Narayana,” Graviton and Anti-Graviton annihilation and creation of
Fermi-Quark and f-meson pair multiplets”, Mathematics Section, Paper No.114,
68th Ind. Sci. Cong. Session, Banaras Hindu University, Varanasi, 3-8th January,
1981.
94. K. L. Narayana,”On the violation of the metric reversal invariance symmetry
and Existance of a new n-Meson”, Symposium on Theoret5ical Studies: Theoretical
Physics Group, Shivaji University, Kolhapur-416004, 12th July 1981.
100. K. L. Narayana,”On certain New Conserved Quantities governing the behavior of
Magneto-fluids in General Relativity”, Paper No.12 : MATSCIENCE: Institute of
Mathematical Sciences, Madras, “Conference on Special and General Relativity and
Applications”, 15th to 21st February 1982.
103. K. L. Narayana,”On Spin-Gravity in a new Renormalization Theory of Electro-
Weak interactions and Gravy-Changing (neutral) Currents existence”, 7th Jan,
Paper No.147, the 69th Sess. of Ind. Sci. Cong. Mathematics Section,
Manasagangotri, (Indian Express 7-1-1982), 1982.
104. K. L. Narayana,”Spinorial Optical Collineations in the General Theory of
Relativity and on Nilch Tensor and Nilch Scalars”, Paper No.54, the 69th Sess. of
Ind. Sci. Cong. Mathematics Section, Manasagangotri, 1982.
105. K. L. Narayana,”An axiomatic Theory of Bio-Cosmos with Bioid Brackets,
Propogation and Invariant Causal structures”, S. N. Bose Institute of Physical
Sciences, International Symposium on Lie-Theoretic Foundations of Mechanics
20th January, 1982, Calcutta.
109. K. L. Narayana,”Magnetic Monopoles, Isorotation and Stream lines of Geodesic
Flow of RMHD in Magnetic Plasma Stars”, 70th Proc. of Ind. Sci. Cong.
Mathematics Section, (Late Paper), Shri Venkateswara University, 5th January,
1983.
110. K. L. Narayana,”On certain new conserved quantities Governing the behavior of
Magneto-fluids in General Relativity”, Paper No. 12: MATSCIENCE, Conf. on
General Relativity and Special Relativity and its Ramifications, 21st December
Mysore, CFTRI, 1982.
111. K. L. Narayana,”On complex angular momenta of Magnetic Plasma Stars and
Gravitational Dyons”, 1st December, Paper No.14,: MATSCIENCE, Conf. on
General Relativity and Special Relativity and its Ramifications, 21st December
Mysore, CFTRI, 1982.
*112. K. L. Narayana,”Stability of Radial Modes and Magnetic Monopoles (Gauge
Quantal ) solutions of Relativistic Plasma Stars”, Gorakhpur, 3-8th November,
Paper No. Proc. of Indian Astronomical Society, 1982.
*113. K. L. Narayana,”Fibre Bundles and a Helical Geometric Differential form
solutions of MHD equations and a Budbudeck Model of Magnetic Monopoles
with Ghosts”, Paper No. ,17th October Symp. on Non-Linear Analysis and
MHD equations, Nanded Science College, Nanded-431602, and
(S. N. Bose Institute, December 1982), 1982.
114. K. L. Narayana,”On Super-Gravity Theories and Meta Physical Models of Hindu
Vaisheshika Philosophy”, AHPS, 5th January, 70th Session of Proc. of Ind. Sci.
Cong., Sri Venkatewswara University, Tirupati, 1983.
115. K. L. Narayana,”Magnetic Monopoles their constituents, GUT and Cosmological
Types of Magnetic Monopoles”, 11th December, Symp/ on Theoretical Studies,
Shivaji Univewrsity, Kolhapur-416004, 1982.
*117. K. L. Narayana,”On Gravitational Invariant Particle Wave Equations in a
Generalized Lyra space, GR-10, Conf. Institute di Fisica, “G.Galilei”,Padova, Italy.
*118. K. L. Narayana, “Gravitational Gauge potentials with twenty-spin-coefficients
and an extended electro-weak theory”, GR-10, Conf. Institute di Fisica
“G.Galilei”, Padov, Italy.
*119. K. L. Narayana, “Quadrupolar Binding of Gravitational free Quarks”,
*119. K. L. Narayana, “Quadrupolar Binding of Gravitational free Quarks”,
GR-10, Conf. Institute di Fisica “G.Galilei” Padov, Italy.
126. K. L.Narayana,” on Spinorial and Materialistic optical Cosmod tensor Invariants
and Cosmod Gravity”, 73rd Sess. Ind. Sci. Cong. Delhi January 6th, Physics
Section, 1986 and 72nd sess. Of Ind. Sci.Cong. Lucknow, Mathematics section,
January 6th, 1985.
*137. K. L. Narayana,”Physical process of Gravitons and Gravy Quark in the interior
of Supergravity Cosmic Stellar structures”, 72nd Session of Ind. Sci. Cong.
January 5th, 1985 and
Arthur Eddington Centenary Symposium, Vol.3, Nagpur, 23rd February 1984.
*138. K. L. Narayana, “Gravitational Instability generated by stochastic process and
New Plasma Waves.” Mathematics section, 73rd Ind. Sci. Cong.
Delhi University, January 5-7th, 1986.
*139. K. L. Narayana, “Relativistic Plasma Instabilities in terms of Nilch and
Electromagnetic potential Twistor fields”,73rd Ind. Sci. Cong.
Delhi University, Jan 5-7th, 1986.
*140. K. L. Narayana, “Dominance of B10 or C12 nuclear production during
Gravitational Collapse in the Stellar Interior?”, Proceedings of Sir
Arthur Eddington Centenary Symposium, Vol.3, Nagpur, 23rd February 1984.
143. K. L. Narayana,”Gravitatiobal Instability generated by Stochastic process and
New Plasma Waves”, Mathematics Section, 73rd Ind. Sci. Cong. Delhi University,
1986.
147. K. L. Narayana, “Physical Process of Gravitons and Gravy Quarks in the Interior
of Supergravity Cosmic stellar structures”, 72nd Sess. Of Ind. Sci. Cong. Lucknow,
January 5th, 1985
and Proc.of Sir Arthur Eddington Centenary Symposium, Vol.3
Nagpur, 23 February, 1984.
148. K. L. Narayana, “A possible Cosmological High Energy Universe”, High Energy
Physics and Astrophysics Int. Conf: University of Kashmir, Srinagar,
Dated 9th September 1987.
149. K. L. Narayana,74th Sess. Ind. Sci. Cong. Bangalore Mathematics section,
(presented) 1987:
(a). “Mathematical Formulation of Stochastic Quark lattice degeneracy and
(a). “Mathematical Formulation of Stochastic Quark lattice degeneracy and
Sum rule selections”, Paper No.65 (Sect.VII)
(b). “The Origin of New Primaries from “Cygnus X-3” and “Centaur”
(b). “The Origin of New Primaries from “Cygnus X-3” and “Centaur”
Astrophysical objects and the Gravy Quark star” Paper No.123,
(Sect.III), Page 68.
(c). “Novel techniques of Potential distributed spinorial (Rangadhama)
(c). “Novel techniques of Potential distributed spinorial (Rangadhama)
Optical quanta ratio thermometry”, Paper No.45, (Sect.III), Page.26.
150. K. L. Narayana,”Gravy Quarks supergravity formulation and Cosmic string
generation of Particles”, Global Conf. on Mathematical Physics (Cent.
Celebrations of Niels Bohr and H. Weyl) Einstein Foundation International
Oct 25, University of Nagpur, (Page.62), 1987.
161. K. L. Narayana,”SPINORIAL-OPTICAL EFFECTS ON THE VIBRATIONS OF
A COLD INCOMPRESSIBLE DIPOLE GAS”,Mathematics Section, 75th Session
of Ind. Sci. Cong. Pune, January, 1988.
*179. Kotcherlakota. L. N. “Waves and Plasma in the Environment of Comets”,
6th Asia Pacific Physics Conference Aug. Kulalampur, Malaysia.
*181.Kotcherlakota. L. N,”A New Model of Upper Atmosphere for the
Indian Southern Peninsular Region and a dynamical Peram Factor Mechanism”,
Paper No.AS01, 36th Congress ISTAM held at Bombay, I.I.T, December 19-22nd,
1991
Also Paper No.72, Proc. 79th Ind. Sci. Cong., Part-III, Physics section) and
K. L. Narayana, Silver Jubl. Symp. “On Variational Methods in Continuum
Mechanics”, Regional Engg. College, Warangal, Mathematics Department,
September 2nd, 1984.
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