Fundamental nuclear structure symmetries in double-beta decay processes

Abstract

Abstract. The nuclear structure physics of double beta decay transitions is reviewed, starting from the consideration of fundamental symmetries of the nuclear many-body problem. The problems found in the use of the quasiparticle random phase approximation (QRPA) and related approximations, in dealing with the calculation of nuclear double beta decay observables, are understood in terms of the mixing between isospin collective and intrinsic variables. I n t r o d u c t i o nYears ago (1988) John Vergados did in fact point out to a number of us that the understanding of the nuclear-structure physics which governs nuclear double beta decay transitions was still a challenging matter and that the currently accepted explanations were in his opinion not very satisfactory. He was indeed right and after ten years the subject remains a hot one, attracting the attention of a very distinguished community of theoretical and experimental groups. I would like to present in this chapter some answers to John's questions as my very modest tribute to his life-long efforts in the fascinating field of the interface between particle and nuclear physics. 2S p o n t a n e o u s a n d D y n a m i c a l B r e a k i n g o f M e a n -F i e l d S y m m e t r i e s i n t h e p n -Q R P A a n d t h e D e s c r i p t i o n o f D o u b l e -B e t a D e c a y T r a n s i t i o n sThe motivations for this part of the present work are the breakdown of the isospin symmetry, at the level of the quasiparticle mean-field approximation, and its partial restoration by effective interactions, at the QRPA level of approximation. The method upon which the discussion is based has been used to define effective symmetry-breaking two-body interactions and it has been applied previously to particle-number and rotational-symmetry violations. We shall also consider the connection between the present approach and the proton-neutron QRPA method with renormalized two-particle interactions. The formalism of the quasiparticle random phase approximation has been used rather intensively and with great success during four decades since the