Instability in relativistic mean-field theories of nuclear matter

Friman, Bengt; Henning, Peter A.

doi:10.1016/0370-2693(88)90699-5

Cited by 34 publications

(28 citation statements)

References 5 publications

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“…Several investigations of finite-size instabilities have been undertaken [8][9][10][22][23][24][25] thus far. However, a systematic analysis of the connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Spurious finite-size instabilities in nuclear energy density functionals

et al. 2013

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It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functional form of the EDF and that can be utilized during the adjustment of its coupling constants. Tuning the coupling constant $C^{\rho \Delta\rho}_{1}$ of the gradient term that triggers scalar-isovector instabilities of the standard Skyrme EDF, we find that the occurrence of instabilities in finite nuclei depends strongly on the numerical scheme used to solve the self-consistent mean-field equations. The link to instabilities of SNM is made by extracting the lowest density $\rho_{\text{crit}}$ at which a pole appears at zero energy in the RPA response function when employing the critical value of the coupling constant $C^{\rho \Delta\rho}_{1}$ extracted in nuclei. Our analysis suggests a two-fold stability criterion to avoid scalar-isovector instabilities: (i) The density $\rho_{\text{min}}$ corresponding to the lowest pole in the RPA response function should be larger than about 1.2 times the saturation density; (ii) one needs to verify that $\rho_{p}(q_{\text{pq}})$ exhibits a distinct global minimum and is not a decreasing function for large transferred momenta.Comment: 9 pages, 11 figures, submitted to Phys. Rev.

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Section: Introductionmentioning

confidence: 99%

Spurious finite-size instabilities in nuclear energy density functionals

et al. 2013

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“…If one adopts this scheme within the Walecka model the free energy would look like the dashed curve in Fig. 1 If instead, like Chin, one adopts the so-called on-mass renormalization scheme the counterterms completely eliminate the total contributions represented by Eqs (14)(15)(16)(17)(18). Within this choice the results are scale independent while M, m s , and m v represent the measurable physical masses at zero density whereas the three and four-body mesonic couplings vanish in agreement with the tree level result displayed by the original Lagrangian density.…”

Section: The Renormalized Vacuum Correction Termmentioning

confidence: 99%

“…This can be achieved by imposing that Γ (3) = Γ (4) = 0 at Λ MS = M in which case the RHA is always reproduced. Finally, in our RG-NLWM inspired prescription we also impose that any Λ MS dependence should be left within the leading logs which naturally emerge within DR, as shown by Eqs (14)(15)(16)(17)(18), and which are the main contributing terms to the β function. In this case, the α 3 and α 4 counterterms also eliminate the Λ MS independent constants in Eqs (17) and (18).…”

Section: The Renormalized Vacuum Correction Termmentioning

confidence: 99%

“…[13] and references therein). At the same time, it has been discussed that approximations of the pure Walecka model are inconsistent leading to an unstable ground state [14] and ignoring the usual nonlinear contributions due to renormalization carries the danger to reenter this instability also in the quantum corrected Walecka model. In principle these facts will spoil any rigorous attempt to include vacuum corrections, in the usual Walecka model, at arbitrarily high orders.…”

Section: Introductionmentioning

confidence: 99%

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Radiatively induced non linearity in the Walecka model

Cavagnoli¹,

Pinto²

2010

Braz. J. Phys.

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We evaluate the effective potential for the conventional linear Walecka non perturbatively up to one loop. This quantity is then renormalized with a prescription which allows finite vacuum contributions to the three as well as four 1PI Green's functions to survive. These terms, which are absent in the standard relativistic Hartree approximation, have a logarithmic energy scale dependence that can be tuned so as to mimic the effects of φ 3 and φ 4 type of terms present in the non linear Walecka model improving quantities such as the compressibility modulus and the effective nucleon mass, at saturation, by considering energy scales which are very close to the nucleon mass at vanishing density.

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“…Studying the possibility of periodic structures, Friman and Henning [4] have investigated the condition of the in-'Present address: Department of Theoretical Physics, Lajos Kossuth University, H-4010 Debrecen, Hungary. stability.…”

Section: Introductionmentioning

confidence: 99%

Periodic structure in nuclear matter

et al. 1992

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The properties of nuclear matter are studied in the framework of quantum hadrodynamics. Assuming an o-meson field, periodic in space, a self-consistent set of equations is derived in the mean-field approximation for the description of nucleons interacting via U-meson and w-meson fields. Solutions of these self-consistent equations have been found: The baryon density is constant in space, however, the baryon current density is periodic. This high density phase of nuclear matter can be produced by anisotropic external pressure, occurring, e.g., in relativistic heavy ion reactions. The self-consistent fields developing beyond the instability limit have a special screw symmetry. In the presence of such an o field, the energy spectrum of the relativistic nucleons exhibits allowed and forbidden bands, similar to the energy spectrum of the electrons in solids. PACS number(s): 21.65. + f

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Instability in relativistic mean-field theories of nuclear matter

Cited by 34 publications

References 5 publications

Spurious finite-size instabilities in nuclear energy density functionals

Spurious finite-size instabilities in nuclear energy density functionals

Radiatively induced non linearity in the Walecka model

Periodic structure in nuclear matter

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