How does ab initio E1 strength change neutron capture rates along nickel isotopes?

The E1 strength adds to rates that M1 alone misses

Neutron capture rates for neutron-rich nuclei feed r-process nucleosynthesis simulations, and many of the relevant nuclei cannot be measured directly. The standard workhorse is the Hauser-Feshbach statistical model, implemented here with the reaction code TALYS, which needs a photon strength function and a nuclear level density as inputs. This paper isolates one input: the electric dipole, or E1, strength near and above the neutron threshold, which the authors compute from first principles rather than taking from a phenomenological model.

The comparison that carries the result is deliberately narrow. The authors compute rates with a phenomenological M1 strength alone, then again with their ab initio E1 strength added on top of that same M1 baseline. The reported enhancement is therefore the effect of adding E1 strength, not a full replacement of all photon strength input. That baseline choice matters: the percentages below describe growth over an M1-only rate, not over a complete rate calculation.

LIT-CC reaches open-shell nickel through a deformed reference

The E1 strength is obtained with the Lorentz integral transform coupled-cluster method, LIT-CC. Coupled-cluster theory builds correlations on top of a Hartree-Fock reference state, and the Lorentz integral transform avoids explicitly constructing the scattering states that make up the continuum response above the particle threshold. Instead, the response is recovered by numerically inverting a transform, which is where a large part of the quoted uncertainty originates.

Closed-shell nuclei allow a spherically symmetric reference, but mid-shell nickel isotopes do not. The authors extend the method to an axially symmetric reference state, where the projection of angular momentum on the symmetry axis, rather than total angular momentum, is a good quantum number. The E1 operator is then handled component by component, and the response is approximated by averaging the three spherical components. The spread between the component with zero projection and the components with projection plus or minus one serves as an estimate of the symmetry-breaking effect, since that difference would vanish in a rotationally invariant calculation.

The calculations use two- and three-nucleon interactions from chiral effective field theory, chiefly the Delta NNLO GO(394) interaction, with the N3LO Texas interaction used for 68Ni and 78Ni to gauge Hamiltonian dependence. The chain covered is 58Ni plus the even-even isotopes 68Ni through 80Ni.

Two data anchors test the method before extrapolation

Before applying the method along the chain, the authors check it against measured quantities. The computed photoabsorption cross section is compared with the measured cross section of 58Ni, and the computed E1 strength is compared with the measured E1 strength of 68Ni. These two anchors are the reason the later neutron-rich predictions are presented as an extension of a tested framework rather than an unconstrained model output.

The 58Ni case also illustrates a subtlety that changes how its rate behaves. For the compound nucleus 58Ni, the first particle threshold is the proton separation energy of 8.17 MeV, several MeV below the neutron separation energy of 12.22 MeV. The E1 strength is therefore probed by transitions to final states below the neutron separation energy plus the incoming neutron energy minus the proton separation energy, which is why the 57Ni(n,gamma)58Ni rate stays sensitive to E1 strength across the whole temperature range considered.

Low-lying E1 strength grows toward the neutron-rich end

Along the chain, the authors find low-lying E1 strength above the neutron threshold in all the even-even isotopes from 68Ni to 80Ni. Its magnitude grows with neutron number, and this growth is the structural reason the rate enhancement also grows with neutron number. The strength near threshold is the part most relevant to neutron capture, because it sits where the photon strength function feeds the capture calculation.

The size of this low-lying strength is currently limited by the inversion of the integral transform. The authors keep a deliberately broad family of admissible inversion solutions, varying the nonlinear parameters and the number of basis functions, and report the envelope as an uncertainty band. They state that a stricter acceptance criterion or a different inversion strategy could reduce this uncertainty in the future. For 78Ni, model-space convergence checks show the transforms at two model-space sizes differ by less than 1% for the transform variable below about 30 MeV, which is the region relevant to the dipole response.

Rates forming 68-78Ni rise between 3 and 10 GK

When the ab initio E1 strength is fed into TALYS, the neutron capture rates forming the even-even isotopes 68Ni through 78Ni are enhanced mainly between 3 and 10 GK. The effect increases with temperature and with neutron number. At the upper edge of the uncertainty band, the enhancement over the M1-only baseline at 5 GK rises from 16% for 67Ni(n,gamma)68Ni to 24% for 77Ni(n,gamma)78Ni. At 10 GK, the corresponding total rates reach 1.8 and 3 times their respective M1-only baselines.

These numbers should be read as an upper-edge estimate within the inversion uncertainty, not as a central value. They also describe a ratio to an M1-only calculation, so they do not by themselves say how far the full rate sits from a measured or library rate. The authors note that their rates agree with the JINA REACLIB and BRUSLIB tabulated rates within one order of magnitude, a spread comparable to typical uncertainties of statistical-model rates in this region, but they describe that comparison as indicative because none of the three rate sets includes full uncertainty quantification.

80Ni shifts the enhancement down to about 0.5 GK

The clearest departure from the chain-wide pattern appears at 80Ni. There, strong pygmy dipole strength lies just above the threshold, and the rate for 79Ni(n,gamma)80Ni departs from the M1-only result already around 0.5 GK. This is a temperature regime well below the 3 to 10 GK window that governs the lighter isotopes in the chain, and it follows directly from where the low-lying strength sits relative to threshold.

The authors also compare their trend with an earlier energy-density-functional study, which quantified the pygmy dipole resonance by a ratio of rates with and without that resonance while retaining the giant dipole resonance in both. The authors caution that their own comparison is different, since they compare the full above-threshold E1 contribution against a calculation without E1 strength, so the two sets of ratios are not directly comparable. What they report as shared is the trend of an increasing E1 effect with neutron number.

The ab initio input stops at the particle threshold

The computed E1 strength covers the response above the first particle emission threshold. Below that threshold, the authors find for the closed-shell 68Ni and 78Ni a single low-lying 1-minus state at about 1 MeV carrying a tiny fraction of the E1 strength, which they judge negligible on the scale of the inversion uncertainty and irrelevant for the capture rates discussed. They did not search for bound states in the open-shell isotopes, because an accurate description in the symmetry-broken framework would require angular-momentum projection, which they leave to future work.

That boundary defines what this paper does and does not deliver. It supplies an ab initio E1 contribution above threshold for a chain of nickel isotopes, not a complete ab initio photon strength function. The M1 part of the strength remains phenomenological in these rate calculations, and the authors identify extending the ab initio description to E1 and M1 strength below the first particle threshold, including the low-energy upbend driven by M1, as a next step requiring angular-momentum projection.

The 80Ni low-temperature enhancement is the case to watch

The paper's most consequential split is not between isotopes in general but between 80Ni and the rest of the chain. For 68Ni through 78Ni, the E1 contribution matters in the 3 to 10 GK window and scales with neutron number, reaching at most a factor of 3 over the M1-only baseline at 10 GK at the upper edge of the uncertainty band. For 80Ni, the pygmy strength just above threshold moves the onset down to roughly 0.5 GK, a different astrophysical regime rather than a larger version of the same effect.

The authors frame the follow-up question accordingly: whether the E1 effects found here, and in particular the low-temperature enhancement for 80Ni, leave an imprint on abundances below mass number 100. That is the specific test this ab initio input enables, and it depends on the low-lying strength near threshold, the inversion uncertainty that currently bounds it, and the temperature at which each isotope's rate actually responds.

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