Complex Spectroscopy

Structure of unstable light nuclei

“…The calculations were performed with an SU(3) shell-model code based on the formalism of French [39] adapted for SU(3) [40]. From the coefficients of the six (0 0) and (2 2) SU(3) tensors which define the central interaction, it is possible find the coefficients of the 5 SU(4) invariants which characterize the symmetry-preserving part of the interaction [41].…”

Shell Model the Monte Carlo Way

“…The basis states are constructed by adding one particle to the anti-symmetrized n -1 states via where +(jn-',/3J') represents the anti-symmetrized basis states with n -1 particles and kn-l(/3, J')j 1 jnaJ] is the coefficient of fractional parentage. One of the first computer codes to implement the CFP procedure is the Oak Ridge Code [29]. Improvements to the general procedure using permutation group symmetries are now being implemented in the Drexel University Shell Model (DUSM) code [30].…”

Shell model monte carlo methods

“…Thus for a general two-body interaction in a general time-reversal invariant form we writê 16) whereÔ α is the time reverse ofÔ α . Since in general, [Ô α ,Ô β ] = 0 we must split the interval β into N t "time slices" of length ∆β ≡ β/N t , 17) and for each time slice n = 1, . .…”

“…[92] ( 64 Zn and 64 Ni). The discussion focuses on the temperature dependence of the internal energy of a nucleus (with proton and neutron numbers Z and N), which is defined as 17) where Ĥ (T ) is the expectation value of the Hamiltonian in the canonical ensemble at temperature T . Guided by the semi-empirical parametrization of the binding energies (e.g., the Bethe-Weizsäcker formula), the difference of U(T ) for two isobars…”

“…Many studies have demonstrated that exact diagonalizations of shell-model Hamiltonians can accurately and consistently describe a wide range of nuclear properties, if the many-body basis is sufficiently large. Pioneering papers include work in the 0p [15], 0s-1d [16] and 0f 7/2 [17] shells; more recent examples are [18,19,20]. Unfortunately, the combinatorial scaling of the many-body space with the size of the single particle basis or the number of valence nucleons restricts such exact diagonalizations to either light nuclei or to heavier nuclei with only a few valence particles [21].…”