Multiphonon nuclear response inO16: A microscopic treatment equivalent to the shell model

Abstract

The electromagnetic response in 16 O is studied within a recently developed approach that generates iteratively a microscopic multiphonon basis well suited for reformulating and solving exactly the nuclear eigenvalue problem within spaces of large dimensions spanned by complex configurations. These multiphonon configurations are seen to modify appreciably, dramatically in some cases, the mean field response. This is shown to be increasingly affected by the center-of-mass motion as the number of phonons increases. The method for removing such a spurious motion is briefly outlined and the effects discussed.

Ground-state correlations within a nonperturbative approach

“…These are a set of generalized eigenvalue equations in the overcomplete basis states |(λ × α) β . Following a procedure [41,42] based on the Cholesky decomposition method, we select a basis of linear independent states |(λ × α) β spanning the physical subspace of the correct dimensions N n < N r and construct a N n × N n nonsingular 024306-3 matrix D n . By left multiplication in the N n -dimensional subspace we get from Eq.…”

“…An explicit and systematic expansion in terms of correlated np-nh states is accomplished in an equation-of-motion phonon method (EMPM) proposed a few years ago [41,42]. In its upgraded version [43], the method constructs a set of equations of motion which are solved iteratively to yield an orthonormal basis of n-phonon states |α n (n = 0,1,2, .…”

Electric dipole response in208Pb within a new microscopic multiphonon approach

“…The redundant states are eliminated by the procedure outlined in [26,27], based on the Cholesky decomposition method. This method selects a basis of linear independent states O † λ |n − 1; α spanning the physical subspace of the correct dimensions N n < N r and, thus, enables us to construct a N n × N n nonsingular matrix D n .…”

“…where C (0) 0 + and C (x) λ are the components of the vacuum |0 and the TDA states |xλ , respectively, and M[0 + → (xλ)] is the TDA transition amplitude (27). The other amplitudes are…”

“…Recently, we developed [25] a new version of an equation of motion phonon method (EMPM) [26,27] which generates iteratively a multiphonon basis built of phonons obtained in the Tamm-Dancoff approximation (TDA) and solves the eigenvalue problem in such a basis. The EMPM adopts a Hamiltonian of general type and treats on the same footing the one-phonon state as well as multiphonon states with any number of phonons.…”