Gyromagnetic Ratio for High Spin Systems

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GYROMAGNETIC RATIO FOR HIGH SPIN SYSTEMS M. Rajasekaran, R. Premanand & D. Caleb Chanthi Raj Department of Nuclear Physics, University of Madras, Guindy Campus, Madras 600 025. The gyromagnetic ratio g^ is c collective nuclear parameter which measures the magnetic properties associated with nucleonic flow. In the simplest versions of nuclear collective models, tho gyromagnetic factor of collective states are expected to be of the order of Z/A, with the assumption that all protons and neutrons take part equally in the collective motion. But the accuracy of the experimental information was in general not good enough to test this property. Theoretically, there are many methods to calculate the g-factors like i) pairing-plus quadrupole approach, the projected Hartree-Fock (PHF) method, the cranked Hartree-Fock-Bogolyubov (CHFB), Interacting boson approximation (IBA), etc. In the present work, we calculate the g-factor by statistical method involving pairing correlation. We calculate g for high spins for various temperatures. In the BCS formalism the equations for particle number, energy, and angular momentum are [1] N - Ii U-(€i-A)tanhtP(Ei-Vmi)/2]/2Ei), (1) 1 2 E = Ei €i{l-<€i-X>tanhlKEi- *roi>/2]/2Ei) - A /G, (2) & I * Zi inij/tl+expJCEi-Vmi) 11 , (3) where E^ * /MGi-A) *A 1 are the quasi-particle energies, €^ and ro^ are the single particle energies and spin projection, G is the pairing strength, A is the gap parameter, P is the reciprocal of the temperature T and X is the chemical potential. The parameters "i, /\ and A are fixed by solving equations (1-3) along with the gap equation Ei tanh[P(Ei-n/mi)/21/2Ei = 2/G. (4) -71- The moment of inertia is given as 2 l 5 = "n I &Erot/dl) ~ (5) where the rotational energy Erot(I) = E(T,I)-E(T,0) The gyroroagnetic ratio is given by 12] = (6) 9R 'n In this work, we.gghave calculated the gyromagnetic ratio for Os nucleus upto the angular momentum states of 20 h for different values of the temperature T = 1.5 to 2.0 MeV. In the figure given below we plot g-factor vs Angular momentum I for^various temperatures. The g2<I=2) value for Os is well reproduced with the experimental value. Further works on the osmium isotopes and rare-earth region are under way. 0.475 T*l-3 0.470 0.465 1L.460 T 0.455 0.450 0 5 10 15 20 0.445 Angular momentum (I) (ft) References; 111 L.G. Moretto, Nucl. Phys. A216 (1973) 1. [21 J.M. Eisenberg and W. Greiner, Microscopic theory of the nucleus, (North-Holland, Amsterdam, 1975) p.383. Work supported UGC-COSIST under SAP. R.P. thanks Govt. of Tamilnadu for the fellowship. -72-.

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