Speaker
Description
The Pandya relation connects the interaction between two particles (or two holes) with the interaction between a particle and a hole [1], and follows from the action of the particle-hole conjugation operator in the context of the shell model [2]. The relation has been used extensively to correlate spectra of pairs of nuclei, for example 40K and 38Cl [3]. Many other examples are known [4,5].
Another useful symmetry of the shell model is seniority, which refers to the number of nucleons that are not in pairs coupled to angular momentum zero [6]. In semi-magic nuclei seniority is an approximate symmetry of the eigenstates of the nuclear Hamiltonian but, more generally, it is a quantum number that can be used to label basis states.
In this talk it is shown that generic expressions of the neutron-proton interaction in a seniority basis reveal a connection with particle-hole conjugation, leading to generalised Pandya relations in terms of 3nj symbols of angular-momentum recoupling coefficients. Examples of its application in nuclei are presented.
[1] S.P. Pandya, Phys. Rev. 103 (1956) 956.
[2] J.S. Bell, Nucl. Phys. 12 (1959) 117.
[3] S. Goldstein and I. Talmi, Phys. Rev. 102 (1956) 589.
[4] R.D. Lawson, Theory of the Nuclear Shell Model (Clarendon, Oxford,1980).
[5] I. Talmi, Simple Models of Complex Nuclei (Harwood, Chur, Switzerland, 1993).
[6] G. Racah, Phys. Rev. 63 (1943) 367; 76 (1949) 1352.
