qanalogue realization of nucleon pairing

Abstract

A q-deformed analogue of zero-coupled nucleon pair states is constructed and the possibility of accounting for pairing correlations examined. For the single orbit case, the deformed pairs are found to be more strongly bound than the pairs with zero deformation, when a real-valued q parameter is used. It is found that an appropriately scaled deformation parameter reproduces the empirical few nucleon binding energies for nucleons in the 1'/Q orbit and 1gQIq orbit. The deformed pairHamiltonian apparently accounts for many-body correlations, the strength of higher-order force terms being determined by the deformation parameter q. An extension to the multishell case, with deformed zero-coupled pairs distributed over several single particle orbits, has been realized.An analysis of calculated and experimental ground state energies and the energy spectra of three lowermost 0+ states, for even-A Ca isotopes, reveals that the deformation simulates the efFective residual interaction to a large extent.

BCS theory ofq-deformed nucleon pairs:qBCS

“…Sn isotopes also indicates that their is a well defined universe of sets of values for pairing strength G and deformation parameter q, for which qBCS converges and has a non-trivial solution. For The results of our present study are consistent with our earlier conclusions [2,8] that the q-deformed pairs with q > 1 (q real) are more strongly bound than the pairs with zero deformation and the binding energy increases with increase in the value of parameter q. In contrast by using complex q values one can construct zero coupled deformed pairs with lower binding energy in comparison with the no deformation zero coupled nucleon pairs [8].…”

“…The quantum group SU q (2), a q-deformed version of Lie algebra SU (2), has been studied extensively [3][4][5], and a q-deformed version of quantum harmonic oscillator developed [6,7]. The quantum group SU q (2) is more general than SU (2) and contains the later as a special case. The underlying idea in using the zero coupled nucleon pairs with q-deformations is that the commutation relations of nucleon pair creation and destruction operators are modified by the correlations as such are somewhat different in comparison with those used in deriving the usual theories.…”

“…In order to include the pairing correlations left out in these approximate schemes, we studied the zero coupled nucleon pairs with q-deformations [2] expressing these in terms of the generators of quantum group SU q (2). The quantum group SU q (2), a q-deformed version of Lie algebra SU (2), has been studied extensively [3][4][5], and a q-deformed version of quantum harmonic oscillator developed [6,7]. The quantum group SU q (2) is more general than SU (2) and contains the later as a special case.…”

Quantum groups and their applications in nuclear physics

“…33.24)). A basic difference is that the deformed theory of 334,335 reduces to the classical theory for q → 1, so that q-deformation is introduced in order to describe additional correlations, while in the present formalism the Q-oscillators involved for Q → 1 reduce to usual harmonic oscillators, so that Q-deformation is introduced in order to attach to the oscillators the anharmonicity needed by the energy expression (eq. (35.6)).…”

Generalizedq-deformed symplecticsp(4) algebra for multi-shell applications

“…While this preserves the underlying symmetry, it introduces non-linear terms into the theory. In contrast with the usual formulation of qdeformation for the symplectic sp(4) algebra and its su (2) subalgebras that is normally used in mathematical studies [10,11,12] and in nuclear physics applications [13,14,15], we have discovered a new formulation that depends upon the dimensionality of the underlying space [16]. Because of this dependence, a generalization of the q-deformed symplectic sp q (4) algebra to a multi-orbit case is an interesting exercise that introduces new elements into the theory.…”