Ground-state Energy Of Nuclear Matter Research Articles

Ground-state energy of nuclear matter.

The low-density expansion of the ground-state energy for spin-dependent forces is given, through order ${k}_{F}^{6}$ for the ladder approximation and through order ${k}_{F}^{6}$ln${k}_{F}$ for the complete energy, in terms of derivatives with respect to the strength of the attractive part of the interaction defined by the Baker-Hind-Kahane potential. The ladder approximation is also computed by the numerical solution of the K-matrix equation. The resulting series gives a satisfactory representation of the energy at interesting densities. Using Pad\'e extrapolation techniques, both in the density and in the attractive part of the interaction, we obtain the ground-state energy of nuclear matter.

Embedding of the Brueckner Approximation in the Extended Jastrow Scheme

A nonperturbative derivation of the Brueckner approximation to the ground-state energy of nuclear matter (with standard choice of hole and particle energies) is given within the framework of the method of correlated basis functions. The structure of the factor-cluster (FIY) expansion of the expectation value of the Hamiltonian with respect to a trial function incorporating short-range correlations in a general fashion, is analyzed for a uniform extended medium of fermions. With a special choice of correlated wave function, the Brueckner approximation is extracted from the FIY expansion by selective summation of two-body combination terms to all orders in the smallness parameter $\ensuremath{\kappa}$ associated, in this case, with both Brueckner-Bethe-Goldstone and FIY energy expansions. A reexamination of the numerical comparison of conventional Brueckner and Jastrow methods carried out earlier for two simple models of nuclear matter leads to the conclusion that it is inadvisable, at least in a Jastrow calculation satisfying the average Pauli condition, to incorporate the $O(\ensuremath{\kappa})$ contribution of the analog of the dispersion correction of reaction-matrix theory without at the same time including the $O(\ensuremath{\kappa})$ contribution of the analog of the Bethe-Faddeev term. For the uniform extended medium for the Jastrow choice of wave function, there is a formal cancellation of these two three-body contributions, the scale of this cancellation being governed by the size of $\ensuremath{\kappa}$. In the numerical example considered, $\ensuremath{\kappa}$ is about 0.22 and the cancellation goes something like +14 MeV-15 MeV=-1 MeV. These findings, when juxtaposed with the standard Brueckner results for the simple models in question, suggest that a departure from the standard prescription of hole and particle energies in reaction-matrix theory may be necessary when $\ensuremath{\kappa}$ is sizeable-as in liquid $^{3}\mathrm{He}$ and the high-density neutron gas, as well as equilibrium nuclear matter described with some potentials.

Hole-Line Expansion for Nuclear Matter

The ground-state energy of nuclear matter is expanded in such a way that each term of the expansion is characterized by the number of hole lines. This procedure reverses the usual sequence of steps, which consists in the use of the linked-cluster theorem, the introduction of $G$ matrices, and the partial summation of $G$-matrix diagrams leading to the hole-line expansion. In this way, we find an algebraic method which yields automatically all diagrams with a fixed number of independent hole lines. As a by-product, a new proof for the linked-cluster theorem is obtained. We have applied the method to diagrams with four independent hole lines and find complete agreement with results published previously by B. D. Day.

Investigation of some long-range force corrections to the ground-state energy of nuclear matter

Some long-range corrections to the ground-state binding energy in nuclear matter are calculated according to Moszkowski-Scott variant of Brueckner's method. The second-order Born term v l ( Q/ e) v l including exchange is calculated. The long-range potential ( v l ) used is the OPEP with a varied cut-off distance. Kinetic energies with an effective mass M ∗ = 0.75 M are used for the single-particle states. The results from the calculation of the correction terms in third and fourth order seem to indicate that the long-range effects do not endanger the cluster expansion. For a typical value of the cut-off distance (1 fm) the energy arising from the exchange part of v l ( Q/ e) v l turns out to be −2.3 MeV, a value which is not negligible compared with the direct contribution −10 MeV.

On the contribution of anomalous diagrams to the ground-state energy of nuclear matter

It is shown that spin-orbit two-nucleon interaction does not lead to anomalous contributions to the Brueckner-Goldstone perturbation series in the second approximation.