Analytic expressions for the Λ energy in the lower nodeless Λ single particle states

1999

EPJ A

Section: Introductionmentioning

confidence: 99%

Mass number dependence in Λ–hypernuclei by means of the Hypervirial Theorems

1999

EPJ A

“…Namely Eq. (13) shows that the lower the excited state the better the approximation , as the parameter L becomes smaller .…”

mentioning

confidence: 98%

“…The similarity between (10) and (7) is obvious . In fact if it wasn't for the centrifugal term of (7) they would have been identical [13]. Note that, for the s-states (l = 0), series (9) is summed up to the well known exact formula for the RPT potential[10]:…”

mentioning

confidence: 99%

“…To assess the accuracy of those formulae two tables have been set up which depict the energy eigenvalues for various Λ−hypernuclei calculated through (13) and (14) respectively, against those calculated a) by a numerical integration of the corresponding Schroedinger equation. b) by means of a perturbation method [12] c) experimentally [28] The parameters of the potentials used here were obtained by fitting procedures to the available experimental data.…”

mentioning

confidence: 99%

“…where R is the nuclear radius of a nucleus with mass number A, assuming a rigid core model. Note that another significant advantage is that the kinetic and the potential energy can be derived readily from (13) and (14) by a simple differentiation with respect to s [14], through Eq. (15).…”

mentioning

confidence: 99%

See 2 more Smart Citations

Two approximate formulae for the binding energies in Λ-hypernuclei and light nuclei

1999

Europhys. Lett.

Two approximate formulae are given for the binding energies in Λ−hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller and the Gaussian central potentials. Those easily programmable formulae combine the eigenvalues of the transformed Jacobi eigenequation and an application of the hypervirial theorems. : 21.80.+a, 21.10.Dr A wealth of experimental results has been produced in an attempt to determine the binding energies of a Λ−hyperon in Λ−hypernuclei defined as: PACS

Application of the quantum mechanical hypervirial theorems to even-power series potentials

Grypeos

1997

Int J Theor Phys

The class of the even-power series potentials, V(r) = -D + E~=0 Vkkkr 2k+2, V0 = to 2 > 0, is studied with the aim of obtaining approximate analytic expressions for the nonrelativistic energy eigenvalues, the expectation values for the potential and kinetic energy operators, and the mean square radii of the orbits of a particle in its ground and excited states. We use the hypervirial theorems (HVT) in conjunction with the Hellmann-Feynman theorem (HFT), which provide a very powerful scheme for the treatment of the above and other types of potentials, as previous studies have shown. The formalism is reviewed and the expressions of the above-mentioned quantities are subsequently given in a convenient way in terms of the potential parameters, the mass of the particle, and the corresponding quantum numbers, and are then applied to the case of the Gaussian potential and to the potential V(r) = -Dlcosh2(rlR). These expressions are given in the form of series expansions, the first terms of which yield, in quite a number of cases, values of very satisfactory accuracy. ~TRODUCTIONVarious approaches can be employed in an effort to obtain approximate expressions for the energy eigenvalues and other quantities of interest for a particle moving in a certain potential. Unfortunately, the majority entail cumbersome calculations of matrix elements or the ingenious deduction of a trial function. These obstacles can be overcome by using the hypervirial theorem (Hirschfelder, 1960) in conjunction with the Hellmann-Feynman theorem, the HVT-HFT method, which could have been labeled as classical, had it not been for the peculiarities of the potential we select each time.