88
W. H. Dickhoff
of the DOM potential leaving all ingredients of the fit to 40 Ca fixed except for
radius parameters. Excellent agreement with the experimental charge density has
been obtained [38] just as earlier for 40 Ca [37].
Recently acquired elastic neutron scattering data and total cross sections for 48 Ca
were published earlier in our large DOM paper [15] but it was at that time not
possible to generate an accurate fit to the differential cross sections at low energy
employing the local implementation of the DOM. Our current non-local DOM
potentials provide increased flexibility that allows for the present excellent fit to
these data. Most of the properties of the first 20 neutrons in this nucleus are already
well-constrained by the fit to the properties of 40 Ca. The additional influence of the
extra 8 neutrons in this nucleus is then further constrained by these elastic scattering
data and total neutron cross sections [15] as well as level structure. The neutron
properties of 48 Ca are of extreme interest to the community since the neutron radius
can be experimentally probed without ambiguity employing parity-violating elastic
electron scattering experiments at Jefferson Lab [45].
To produce a theoretical error for our result for the neutron skin we have
employed a method that was explored in the determination of the Chapel-Hill global
optical potential [46]. These results have now been published in [38] with our
neutron skin prediction of 0.249±0.023 fm which is much larger than the prediction
of the ab initio coupled-cluster calculation reported in [47] and most mean-field
calculations [48]. We note that this work fulfills the earlier promise of the DOM,
in that it can be employed to make sensible predictions of important quantities
constrained by other experimental data. When envisaged earlier [35], it was thought
that these predictions would involve only rare isotopes but important quantities for
stable nuclei also fall under its scope. We show in Fig. 3 results for the neutron
skin of 48 Ca plotted versus the one of 208 Pb as presented in [48], while adding
horizontal bars for the DOM result [38] and the coupled-cluster result of [47]. Our
current efforts for 208 Pb are also generating a large neutron skin as indicated by the
large square in Fig. 3. The dashed box includes the central value of [49] but with
the expected error of the PREX-II experiment. The expected error for the CREX
experiment [45] is indicated by the vertical width of the box while its central value
is arbitrarily chosen.
5 Conclusions
As illustrated in this paper, the DOM provides ingredients for transfer reactions,
the (e, e p) reaction, and predictions for the neutron skin of 48 Ca and 208 Pb,
demonstrating the relevance of this approach to simultaneously answer the questions
how nucleons propagate through the nucleus at positive energy and where they are
localized in the ground state. Extensions to other knockout reactions like (p, pN)
and the improved description of the deuteron will likely contribute to a robust
extension of the DOM to rare isotopes.
W. H. Dickhoff
of the DOM potential leaving all ingredients of the fit to 40 Ca fixed except for
radius parameters. Excellent agreement with the experimental charge density has
been obtained [38] just as earlier for 40 Ca [37].
Recently acquired elastic neutron scattering data and total cross sections for 48 Ca
were published earlier in our large DOM paper [15] but it was at that time not
possible to generate an accurate fit to the differential cross sections at low energy
employing the local implementation of the DOM. Our current non-local DOM
potentials provide increased flexibility that allows for the present excellent fit to
these data. Most of the properties of the first 20 neutrons in this nucleus are already
well-constrained by the fit to the properties of 40 Ca. The additional influence of the
extra 8 neutrons in this nucleus is then further constrained by these elastic scattering
data and total neutron cross sections [15] as well as level structure. The neutron
properties of 48 Ca are of extreme interest to the community since the neutron radius
can be experimentally probed without ambiguity employing parity-violating elastic
electron scattering experiments at Jefferson Lab [45].
To produce a theoretical error for our result for the neutron skin we have
employed a method that was explored in the determination of the Chapel-Hill global
optical potential [46]. These results have now been published in [38] with our
neutron skin prediction of 0.249±0.023 fm which is much larger than the prediction
of the ab initio coupled-cluster calculation reported in [47] and most mean-field
calculations [48]. We note that this work fulfills the earlier promise of the DOM,
in that it can be employed to make sensible predictions of important quantities
constrained by other experimental data. When envisaged earlier [35], it was thought
that these predictions would involve only rare isotopes but important quantities for
stable nuclei also fall under its scope. We show in Fig. 3 results for the neutron
skin of 48 Ca plotted versus the one of 208 Pb as presented in [48], while adding
horizontal bars for the DOM result [38] and the coupled-cluster result of [47]. Our
current efforts for 208 Pb are also generating a large neutron skin as indicated by the
large square in Fig. 3. The dashed box includes the central value of [49] but with
the expected error of the PREX-II experiment. The expected error for the CREX
experiment [45] is indicated by the vertical width of the box while its central value
is arbitrarily chosen.
5 Conclusions
As illustrated in this paper, the DOM provides ingredients for transfer reactions,
the (e, e p) reaction, and predictions for the neutron skin of 48 Ca and 208 Pb,
demonstrating the relevance of this approach to simultaneously answer the questions
how nucleons propagate through the nucleus at positive energy and where they are
localized in the ground state. Extensions to other knockout reactions like (p, pN)
and the improved description of the deuteron will likely contribute to a robust
extension of the DOM to rare isotopes.