Gogny D1M Effective Interaction

• Gogny D1M is a parametrization of the finite-range, density-dependent force used in self-consistent HFB calculations to reproduce binding energies and charge radii.
• It employs a two-Gaussian central form with a zero-range density-dependent and spin–orbit term, naturally generating both particle–hole and pairing fields.
• D1M demonstrates robust performance in finite nucleus, fission, and beyond-mean-field studies, though its softer neutron matter equation of state has inspired reparametrizations for astrophysical use.

to=arxiv_search.search 银航json {"^^^^^^^^10query10 D1M effective interaction D1M Gogny arXiv10^^^^^^^^", "^^^^^^^^10max_results10 ^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^} to=arxiv_search.search ＿国产json {"^^^^^^^^10query10 or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^^^^^", "^^^^^^^^10max_results10 ^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^} to=arxiv_search.search 天天彩票中大奖json {"^^^^^^^^10query10 state octupole correlation energies with effective forces^^^^^^^^10\10 OR ^^^^^^^^10\10 field study of structural changes in Pt isotopes with the Gogny interaction^^^^^^^^10\10 OR ^^^^^^^^10\10 finite-size instabilities with Gogny-type interactions^^^^^^^^10\10 "^^^^^^^^10max_results10 ^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^} to=arxiv_search.search 全民彩票天天送钱json {"^^^^^^^^10query10 Gogny D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M", "^^^^^^^^10max_results10 ^^^^10max_results10^^^^} The Gogny D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M effective interaction is a parametrization of the finite-range, density-dependent Gogny force used in self-consistent Hartree–Fock–Bogoliubov calculations of nuclear structure. Within the D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^ family, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M was adjusted to reproduce all known nuclear binding energies using HFB, supplemented by an approximate rotational energy correction and an approximate zero-point energy correction associated with quadrupole motion, while also constraining charge radii and requiring a realistic symmetric and neutron-matter equation of state; the resulting global mass fit achieved an rms deviation of ^^^^10query10^^^^.^^^^10\10 OR \10^^^^ MeV (&&&^^^^10query10^^^^&&&). In subsequent applications, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M has been used as a global Gogny energy density functional for mean-field, beyond-mean-field, fission, spectroscopic, and astrophysical studies, with the same finite-range interaction generating both the particle–hole and pairing fields (&&&^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^&&&).

^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^. Historical placement and fitting rationale

D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M was introduced as a successor to earlier Gogny parametrizations such as D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^N, with an explicit emphasis on global mass reproduction and realistic matter properties. In the fission literature, it is described as a parametrization designed to improve global nuclear mass predictions relative to D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S while maintaining good spectroscopic performance, and as curing the “mass drift” of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S in heavy nuclei and improving PRESERVED_PLACEHOLDER_^^^^10query10^^^^ values (&&&^^^^10max_results10^^^^&&&). In large-scale fission benchmarks, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is further characterized as fitted to realistic neutron matter and to the binding energies of all known nuclei, achieving a global rms of ^^^^10query10^^^^.^^^^10\10 OR \10 OR \10^^^^ MeV (&&&^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^&&&).

The fit strategy is central to the identity of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M. One strand of the literature emphasizes that the parameters were adjusted to reproduce all known nuclear binding energies with HFB, supplemented by approximate rotational and quadrupole zero-point corrections, in the spirit of a ^^^^10max_results10^^^^D Bohr Hamiltonian (&&&^^^^10query10^^^^&&&). Another strand stresses that the fit also incorporated a realistic neutron-matter equation of state and charge radii, making D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M simultaneously a mass model and a constrained effective interaction for bulk matter (&&&^^^^10max_results10^^^^&&&). This construction explains why D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is often chosen when binding-energy systematics, neutron-rich nuclei, or heavy-nucleus fission are the primary targets.

A recurring conclusion across applications is that D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M preserves the characteristic robustness of the Gogny framework. In Pt isotopes, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M yields results extremely similar to those of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^N, with only modest quantitative differences traceable to pairing strength and barrier heights (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^&&&). In octupole-correlation studies, the qualitative and quantitative conclusions obtained with D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M are reported to be similar to those found with D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^N (&&&^^^^10query10^^^^&&&). This suggests that D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is best understood not as a radical departure from the Gogny tradition, but as a refit that shifts the balance toward global masses and matter constraints.

^^^^10max_results10^^^^. Formal structure of the interaction

D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M retains the standard Gogny operator structure: two finite-range Gaussian central terms with spin- and isospin-exchange operators, a zero-range density-dependent term, and a zero-range spin–orbit term; in finite nuclei, the Coulomb interaction is included for protons (&&&^^^^10query10^^^^&&&). In conventional notation, the two-body interaction is written as

PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^

with PRESERVED_PLACEHOLDER_^^^^10max_results10^^^^ and PRESERVED_PLACEHOLDER_^^^^10query10^^^^ the spin and isospin exchange operators, PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^ the Gaussian ranges, PRESERVED_PLACEHOLDER_^^^^10max_results10^^^^ the local density, and PRESERVED_PLACEHOLDER_^^^^10query10^^^^ the relative-momentum operators acting to the right and left (&&&^^^^10query10^^^^&&&).

The D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M parameter set reported in later Gogny neutron-star work is

PRESERVED_PLACEHOLDER_^^^^10\10^^^^

PRESERVED_PLACEHOLDER_^^^^10 OR \10^^^^

PRESERVED_PLACEHOLDER_^^^^10 OR \10^^^^

PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^

(&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^&&&). The literature also writes the density-dependent exchange coefficient as PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10Gogny D1M effective interaction D1M Gogny arXiv10^^^^ rather than PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10max_results10^^^^; both notations appear in Gogny papers collected here.

A defining technical feature of the Gogny architecture is that the same finite-range interaction generates both the mean field and the pairing field. In HFB applications with D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M, no separate pairing force is introduced, and the finite range makes the pairing tensor finite and naturally regulates ultraviolet behavior (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^&&&). This aspect distinguishes D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M from functionals in which pairing is appended phenomenologically.

^^^^10query10^^^^. Nuclear-matter properties and global EDF character

The bulk properties of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M at saturation are explicitly tabulated in unified neutron-star calculations: saturation density PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^, energy per particle PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^, incompressibility PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10max_results10^^^^, isoscalar effective mass PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^, symmetry energy PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10\10^^^^, symmetry energy at PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^ of PRESERVED_PLACEHOLDER_^^^^10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^, and slope parameter PRESERVED_PLACEHOLDER_^^^^10max_results10query10^^^^ (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^&&&). These numbers are consistent with the broader characterization of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M as a Gogny functional that combines good finite-nucleus performance with a realistic symmetric and neutron-matter equation of state (&&&^^^^10query10^^^^&&&).

The same body of work also identifies a limitation: D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M produces a rather soft equation of state in neutron matter, and in neutron-star applications this softness leads to a maximum mass of about PRESERVED_PLACEHOLDER_^^^^10max_results10Gogny D1M effective interaction D1M Gogny arXiv10^^^^, below the observational value of two solar masses (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^&&&). Earlier astrophysical discussions make the same point more generally for D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^N, and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M, noting that the common problem is a too soft neutron-matter equation of state at high density (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^&&&). The issue is therefore not a defect of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M in finite nuclei, but a tension between finite-nucleus calibration and the high-density isovector sector.

This limitation motivated reparametrizations derived from D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M. D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M** were constructed by modifying the finite-range strengths so as to stiffen the symmetry energy density dependence while preserving the good properties of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M in finite nuclei (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^&&&, &&&^^^^10max_results10query10^^^^&&&, &&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^&&&). The reparametrization strategy kept PRESERVED_PLACEHOLDER_^^^^10max_results10max_results10^^^^, PRESERVED_PLACEHOLDER_^^^^10max_results10query10^^^^, and the spin–orbit strength fixed, constrained symmetric-matter properties and pairing combinations to remain equal to D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M, and used the remaining freedom to increase PRESERVED_PLACEHOLDER_^^^^10max_results10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^ (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^&&&). The relation between D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* is therefore structural: D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* is best viewed as a targeted isovector modification of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M rather than an unrelated force.

^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^. Mean-field and beyond-mean-field implementation

D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is used within the constrained HFB framework in both axial and triaxial spaces. In representative calculations, the HFB equations are solved in a harmonic-oscillator basis with a gradient method to locate minima, with constraints imposed on multipole operators such as PRESERVED_PLACEHOLDER_^^^^10max_results10max_results10^^^^, PRESERVED_PLACEHOLDER_^^^^10max_results10query10^^^^, and PRESERVED_PLACEHOLDER_^^^^10max_results10\10^^^^ (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^&&&). In octupole applications, a family of axially symmetric HFB states PRESERVED_PLACEHOLDER_^^^^10max_results10 OR \10^^^^ is generated by varying the axial octupole moment, and the constrained energy

PRESERVED_PLACEHOLDER_^^^^10max_results10 OR \10^^^^

is used to determine whether the ground state spontaneously breaks reflection symmetry (&&&^^^^10query10^^^^&&&).

Beyond mean field, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M has been employed in parity restoration and in Generator Coordinate Method calculations. For parity projection one evaluates

PRESERVED_PLACEHOLDER_^^^^10query10query10^^^^

while in the GCM the collective state is written as

PRESERVED_PLACEHOLDER_^^^^10query10Gogny D1M effective interaction D1M Gogny arXiv10^^^^

with the weights determined by the Hill–Wheeler equation (&&&^^^^10query10^^^^&&&). In more elaborate quadrupole–octupole studies, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is combined with parity restoration and symmetry-conserving GCM in two collective coordinates, using mixed-density or projected-density prescriptions for the density-dependent term (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^&&&).

This methodology has two implications for the interpretation of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M. First, the parametrization is routinely deployed not only as a static mean-field interaction but as a building block for correlation energies, negative-parity excitations, and collective amplitudes. Second, the density dependence of Gogny forces requires explicit care in symmetry restoration and configuration mixing, a point repeatedly emphasized in the D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M literature [(&&&^^^^10query10^^^^&&&); (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^&&&)].

^^^^10max_results10^^^^. Finite-nucleus applications and empirical performance

In large-scale octupole studies over ^^^^10 OR \10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^ even–even nuclei from oxygen to copernicium, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M yields modest but non-negligible octupole correlation energies: the mean-field octupole energy gain does not exceed about PRESERVED_PLACEHOLDER_^^^^10query10max_results10^^^^ MeV, parity-restored correlation energies reach up to about PRESERVED_PLACEHOLDER_^^^^10query10query10^^^^ MeV, and full octupole GCM correlation energies reach up to about PRESERVED_PLACEHOLDER_^^^^10query10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^ MeV (&&&^^^^10query10^^^^&&&). When these correlations are added to binding energies, they tend to shift theoretical curves upward almost uniformly, with only minor local improvements; the too-large shell gaps predicted by self-consistent mean-field models are not quenched (&&&^^^^10query10^^^^&&&). The specific conclusion is that octupole correlations do not affect in a significant way the trend and systematic of binding energies.

In Pt isotopes, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M reproduces the same qualitative and nearly the same quantitative mean-field structural systematics as D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^N. The robust picture reported there is: PRESERVED_PLACEHOLDER_^^^^10query10max_results10^^^^Pt prolate ground states, PRESERVED_PLACEHOLDER_^^^^10query10query10^^^^Pt triaxial PRESERVED_PLACEHOLDER_^^^^10query10\10^^^^-soft ground states, PRESERVED_PLACEHOLDER_^^^^10query10 OR \10^^^^Pt oblate ground states, and PRESERVED_PLACEHOLDER_^^^^10query10 OR \10^^^^Pt spherical (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^&&&). The differences relative to D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^S are limited to slightly lower spherical barrier heights and stronger pairing, the latter leading to somewhat smaller Thouless–Valatin moments of inertia (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^&&&). This close agreement is one of the clearest demonstrations that D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M preserves Gogny spectroscopic systematics outside the mass-fit dataset.

Fission applications extend the range of validation. For uranium isotopes PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10query10^^^^U, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is benchmarked against available experimental data on inner and second barrier heights, excitation energies of the fission isomers, and half-lives, and is concluded to represent a reasonable starting point to describe fission in heavy and superheavy nuclei (&&&^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^&&&). For plutonium isotopes PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10Gogny D1M effective interaction D1M Gogny arXiv10^^^^Pu, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is again described as a reasonable starting point for microscopic fission, with the important caveat that absolute spontaneous-fission half-lives are extremely sensitive to pairing strength and collective inertia (&&&^^^^10max_results10^^^^&&&). In both uranium and plutonium studies, the trends with neutron number are reproduced more reliably than the absolute values.

D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M has also served as the microscopic input to mapped spectroscopic models. In odd-odd PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10max_results10^^^^Cs, constrained Gogny-D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M HFB calculations provide the PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10query10^^^^-deformation energy surfaces of the even-even Xe cores, as well as single-particle energies and occupation probabilities, which are then mapped to an interacting boson–fermion–fermion Hamiltonian (&&&^^^^10query10max_results10^^^^&&&). This use underscores a broader role of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M: it is not only a direct HFB interaction, but also a generator of microscopic structure inputs for algebraic or collective Hamiltonians.

^^^^10query10^^^^. Stability, misconceptions, and descendant parametrizations

A recurrent misconception is to transfer the finite-size-instability discussion of D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* to D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M itself. The linear-response study of Gogny-type interactions reports that D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M performs better than D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^N in the scalar–isovector channel, and finite-nucleus tests confirm the absence of spurious behavior for D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M (&&&^^^^10max_results10^^^^&&&). In coordinate-space calculations for PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^Pb, PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10max_results10^^^^Sn, and PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10query10^^^^He, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M converges and yields physically reasonable proton and neutron densities (&&&^^^^10max_results10^^^^&&&). The instability problem identified in ^^^^10max_results10query10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^ is therefore specific to D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* and, to a lesser extent, D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^N, not to D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M.

The subsequent comment on D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* sharpened that distinction. It independently confirmed the existence of a finite-size instability for D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* in coordinate-space calculations, but also showed that harmonic-oscillator-basis calculations—the standard framework for Gogny forces—are robust, and that beyond-mean-field GCM calculations with D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* remain stable and yield results very close to D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M (&&&^^^^10query10 OR \10^^^^&&&). For D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M itself, the same comment presents consistent HO-basis and mesh binding energies for doubly magic nuclei, reinforcing the view that D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is a stable reference within the Gogny family.

In astrophysical work, the D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M descendants D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M** were introduced precisely because D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M is too soft in neutron matter, not because it is unreliable in finite nuclei (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10 OR \10^^^^&&&, &&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^&&&). D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* raises the symmetry-energy slope to PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10\10^^^^ MeV and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M** to PRESERVED_PLACEHOLDER_^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10 OR \10^^^^ MeV, producing maximum neutron-star masses around two solar masses while preserving D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M-like finite-nucleus performance (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^&&&). A plausible implication is that D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M remains the reference Gogny parametrization when global finite-nucleus structure is the priority, whereas D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M* and D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M** are specialized extensions for neutron-star applications.

Taken together, the literature presents D^^^^10Gogny D1M effective interaction D1M Gogny arXiv10^^^^M as a global Gogny effective interaction with a canonical two-Gaussian finite-range structure, a density-dependent zero-range term, and a zero-range spin–orbit term; a fit protocol centered on masses, radii, and matter constraints; strong performance in mean-field and beyond-mean-field finite-nucleus calculations; and a well-defined limitation in the high-density isovector sector that later reparametrizations sought to remedy [(&&&^^^^10query10^^^^&&&); (&&&^^^^10(Robledo, 2014) or (Rodriguez-Guzman et al., 2010) or (Martini et al., 2018) Gogny D1M10^^^^&&&); (&&&^^^^10Gogny D1M effective interaction D1M Gogny arXiv10query10^^^^&&&)].