A simple derivation of a closed formula for Bogoliubov boson transformations

Abstract

Considering the states with an arbitrary number of bosons and their transformed states under Bogoliubov transformations as wavefunctions of an oscillator type, a very simple derivation for the matrix elements of the Bogoliubov transformations is given.

New results about the canonical transformation for boson operators

“…We recall that we use the Bargmann representation and therefore the vacuum state normalized to unity is |0 = 1 This expression (3.13) is identical to those obtained in Refs. [11][12][13] by more tedious methods.…”

“…To each type of boson-s, initial or transformed, one associates a basis generating two boson spaces, respectively. Long time ago, the unitary transformation connecting the mentioned bases was analytically expressed [11][12][13].…”

Toward a microscopic description of theM1 states in deformed even-odd nuclei

“…Apart from an additive constant, the boson mapping of the model Hamiltonian H (1) for the core is H .... =ZCOkB;Bk (25) k Adding few terms of higher order in bosons to H, we (AAR and his collaborators) have evaluated in [22] the corresponding corrections to the RPA energies and B(M1)T values 9 The main effect of the higher order terms is to reduce fragmentation 9 In this respect they counterbalance the spin-orbit effect. We also give therein arguments for the angular momentum assignment of the two RPA states, which is very relevant for our present purposes 9 We have presented so far the main features of the core system as described by the RPA formalism 9 They will be used in the next section in defining the particle-core coupling picture 9…”