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arxiv: 2606.12253 · v1 · pith:5CEUCIXJnew · submitted 2026-06-10 · ⚛️ nucl-th · nucl-ex

Recent applications of the subtracted second RPA method

Danilo Gambacurta , Marcella Grasso This is my paper

Pith reviewed 2026-06-27 08:02 UTC · model grok-4.3

classification ⚛️ nucl-th nucl-ex
keywords SSRPASRPAnuclear excitationsenergy density functionalRPAcharge-exchangegiant resonancesnuclear equation of state
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The pith

The subtracted second RPA overcomes pathological issues in the second RPA within energy density functional theory and improves agreement with experimental data for nuclear excitations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews recent applications of the subtracted second random phase approximation (SSRPA), which is designed to fix problems that arise when the second RPA is used together with energy density functionals. Standard SRPA can lead to unphysical results such as instabilities or incorrect excitation energies in nuclear systems. By applying a subtraction procedure, SSRPA eliminates these issues while retaining the ability to describe collective excitations. The authors show applications to both charge-conserving and charge-exchange excitations, where SSRPA provides better matches to experimental data than RPA or SRPA. They also explore how the induced correlations affect the modeling of the nuclear equation of state.

Core claim

SSRPA overcomes the pathological issues encountered by SRPA within Energy Density Functional theory and yields improved agreement with experimental data for both charge-conserving and charge-exchange nuclear excitations.

What carries the argument

The subtraction procedure applied to the second RPA response function, which removes the anomalous contributions responsible for instabilities in SRPA calculations.

If this is right

  • SSRPA calculations remain stable without unphysical negative energies or divergences.
  • Quantitative agreement with experimental spectra improves for giant resonances and other collective modes.
  • Beyond-mean-field correlations provide better constraints on the nuclear equation of state.
  • The method applies equally to isoscalar and isovector nuclear excitations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The subtraction idea could be tested in other many-body frameworks that suffer from similar double-counting instabilities.
  • Improved excitation energies might tighten predictions for nuclear reactions in astrophysical environments.
  • Numerical scaling studies could check whether SSRPA remains feasible for heavier nuclei.

Load-bearing premise

The subtraction procedure removes the pathologies of SRPA while preserving its physical content without introducing new uncontrolled approximations or artifacts.

What would settle it

An SSRPA calculation that still produces negative excitation energies or diverges for a case where experimental data is available would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.12253 by Danilo Gambacurta, Marcella Grasso.

Figure 1.1
Figure 1.1. Figure 1.1: Panel (a), top: ISGQR spectrum of the 208Pb(e, e’) reac￾tion. Right: squares of the wavelet coefficients from the CWT. Left: projection of the wavelet coefficients in arbitrary units. The results ob￾tained, in RPA (panel (b)), and in SRPA (panel (a)) are shown. The arrows indicate characteristic scales. Adapted from Ref. [6]. Without aiming to be exhaustive, we recall some of the most advanced many-body … view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: Panel (a): CWT analysis of the photoabsorption s [PITH_FULL_IMAGE:figures/full_fig_p008_1_2.png] view at source ↗
Figure 1.3
Figure 1.3. Figure 1.3: Left column: Equivalent photoabsorption spect [PITH_FULL_IMAGE:figures/full_fig_p009_1_3.png] view at source ↗
Figure 1.4
Figure 1.4. Figure 1.4: Wavelet Analysis of ISGMR strength in 90Zr (left side) and 208Pb (right side). The first row shows the experimentally measured strength followed by four different model predictions. The right column presents the corresponding power spectra determined by summing wavelet coefficients (dashed lines). Scale positions are shown by filled circles with errors. Experimental scales are represented by vertical gra… view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: The RPA (blue dashed lines) and SRPA (full red lin [PITH_FULL_IMAGE:figures/full_fig_p025_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: IVGDR transition strength distribution of [PITH_FULL_IMAGE:figures/full_fig_p026_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Left: Fragmentation of the | (νp3/2)(ν0p3/2)−1 i0+ configurations in the 0+ response of 16O in (a) SRPA, (b) RPA. Thin dark bars show the spectroscopic strength defined in Eq. (3.1), thicker bars denote the distribution of | (ν1p3/2)(ν0p3/2) −1 i0+ (one particle shell only). Right: IVGDR transition strength distribution of 40Ca in RPA (black bars) and SRPA (cyan bars) are shown. Left Figure adapted from … view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Isoscalar monopole response of 16O, calculated within the RPA, SRPA and SRPA in the diagonal approximation (SRPA0) as a function of the excitation energy, in linear (panel (a)) and logarithmic scale (panel (b)). From Ref. [72]. y-scale is different, to make more visible the large amount SRPA states which are much more than in RPA. It is interesting to see the effect of the diagonal approximation with the… view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Left: Isovector dipole response of 16O obtained in RPA (full solid red line), SRPA (dash-dotted cyan line) and SRPA in diagonal approximation (dashed black line).) Right: Monopole component of the double dipole resonance of 16O, obtained in SRPA (solid thick black line) and SRPA0 (diagonal approximation, solid thin cyan line). The unperturbed response is also shown as a reference (black dashed line). Lef… view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: Left: Energies of the four 0+ lowest eigenstates (axis on the left) and percentage of 2p − 2h states(axis on the right) as a function of the energy cutoff E2p2h. Right: Isoscalar (IS) and isovector (IV) dipole strength distributions of 16O. The left y-axis refers to the isoscalar strength and the right one to the folded isovector distributions. Adapted from Ref. [72]. m1(T = 0) m1(T = 1) ωmax SRPA SRPA 4… view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: Isoscalar (upper panel) and isovector (lower pa [PITH_FULL_IMAGE:figures/full_fig_p030_3_7.png] view at source ↗
Figure 3.8
Figure 3.8. Figure 3.8: RPA, dashed (black) lines and SRPA, full (red) li [PITH_FULL_IMAGE:figures/full_fig_p031_3_8.png] view at source ↗
Figure 3.9
Figure 3.9. Figure 3.9: Left:Isoscalar (upper panel) and isovector (lo [PITH_FULL_IMAGE:figures/full_fig_p031_3_9.png] view at source ↗
Figure 3.10
Figure 3.10. Figure 3.10: Comparison between RPA, dashed (black) lines, [PITH_FULL_IMAGE:figures/full_fig_p032_3_10.png] view at source ↗
Figure 3.11
Figure 3.11. Figure 3.11: Left side: SRPA isoscalar dipole strength dist [PITH_FULL_IMAGE:figures/full_fig_p033_3_11.png] view at source ↗
Figure 3.12
Figure 3.12. Figure 3.12: Comparison between RPA (full lines) and SRPA (d [PITH_FULL_IMAGE:figures/full_fig_p033_3_12.png] view at source ↗
Figure 3.13
Figure 3.13. Figure 3.13: Left and center: GT strength distribution obta [PITH_FULL_IMAGE:figures/full_fig_p034_3_13.png] view at source ↗
Figure 3.14
Figure 3.14. Figure 3.14: GT strength distribution as a function of excit [PITH_FULL_IMAGE:figures/full_fig_p035_3_14.png] view at source ↗
Figure 3.15
Figure 3.15. Figure 3.15: Left side: Folded isoscalar strength distribu [PITH_FULL_IMAGE:figures/full_fig_p036_3_15.png] view at source ↗
Figure 3.16
Figure 3.16. Figure 3.16: Isoscalar 0+ response in 16O calculated with the Gogny-RPA (full line) and with the SRPA (panel a) and SRPA* (panel b) approach with an energy cutoff on the 2p − 2h config￾urations of 60 (dotted line) and 80 (dashed line) MeV. Adapted from Ref. [86]. While computationally more intensive than employing a zero￾range interaction, the use of a finite-range force offers several key advantages. Firstly, the G… view at source ↗
Figure 3.17
Figure 3.17. Figure 3.17: Isoscalar monopole response in 16O calculated in the SRPA* case with cutoff energies of 80 (dotted line), 100 (dot￾dashed line) and 120 (dashed line) MeV. Adapted from Ref. [86]. The Coulomb and spin-orbit contributions were omitted from the residual interaction, producing ≃ 5% violation of the EWSR within the RPA. In constructing the 2p − 2h space, all configu￾rations with unperturbed energies below a … view at source ↗
Figure 3.18
Figure 3.18. Figure 3.18: Isoscalar monopole distributions in 16O calculated within the SRPA (panel (a)) and SRPA* (panel (b)) model (dashed lines), compared with the RPA ones. The comparison with the corresponding spectra obtained in the diagonal approximation (dot-dashed lines) is shown. Adapted from Ref. [86]. For the SRPA* calculations, where reasonable conver￾gence with respect to the 2p − 2h space cutoff is achieved and th… view at source ↗
Figure 3.19
Figure 3.19. Figure 3.19: Left side: Lowest eigenvalue of the A ± B matrices in the 1 − channel of 16O within SRPA a function of the 2p − 2h energy cutoff. Right side: 2+ channel of 48Ca within SRPA for increasing number of the 2p − 2h configurations, shown in the upper panel as a function of the cutoff energy E2p−2h. In the lower panel (b), the lowest eigenvalue of the A ± B and A matrices is shown. See the text for more detail… view at source ↗
Figure 3.20
Figure 3.20. Figure 3.20: Left side: the energy-weighted sums m1 and spurious-state-only contributions for various dipole (isovector in panel (a) and isoscalar in panel (b)) operators in 16O within SRPA and SRPA in diagonal approximation SRPA(0), as a function of the 2p−2h energy cutoff. Right side: The non-energy-weighted sums m0 and spurious-state-only contributions for the 1− channel of 16O obtained in SRPA, for (panel (a) th… view at source ↗
Figure 3.21
Figure 3.21. Figure 3.21: (a) Deviations from the RPA energy-weighted su [PITH_FULL_IMAGE:figures/full_fig_p042_3_21.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Isoscalar monopole (left side ) and quadrupole ( [PITH_FULL_IMAGE:figures/full_fig_p043_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Left side: Isoscalar monopole response for [PITH_FULL_IMAGE:figures/full_fig_p044_4_2.png] view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Left side: First 0+ (a) and 2+ (b) states for 16O calculated with the standard SRPA, the SSRPAF , and the SSRPAD, with different cutoffs in the correction terms (in parentheses). Right side: Comparison of values from the standard SRPA, the SSRPAF , the RPA, and experiment for the energy of the first low–lying 0+ (a) and 2+ (b) states. Adapted from Ref. [92]. 44 [PITH_FULL_IMAGE:figures/full_fig_p044_4_3.png] view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Isoscalar monopole (left side ) and quadrupole ( [PITH_FULL_IMAGE:figures/full_fig_p045_4_4.png] view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Panel (a): comparison between the Gogny-RPA, SR [PITH_FULL_IMAGE:figures/full_fig_p046_4_5.png] view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Isoscalar (left side) and isovector (right side [PITH_FULL_IMAGE:figures/full_fig_p047_4_6.png] view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: As in Figure [PITH_FULL_IMAGE:figures/full_fig_p047_4_7.png] view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: As in Figure [PITH_FULL_IMAGE:figures/full_fig_p048_4_8.png] view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: Left side: Monopole strength distribution comp [PITH_FULL_IMAGE:figures/full_fig_p049_4_9.png] view at source ↗
Figure 4.10
Figure 4.10. Figure 4.10: Neutron and proton transition densities multi [PITH_FULL_IMAGE:figures/full_fig_p050_4_10.png] view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: Neutron and proton transition densities multi [PITH_FULL_IMAGE:figures/full_fig_p050_4_11.png] view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: Left side: Monopole isoscalar strength distri [PITH_FULL_IMAGE:figures/full_fig_p051_4_12.png] view at source ↗
Figure 4.13
Figure 4.13. Figure 4.13: Left side: Monopole isoscalar strength distri [PITH_FULL_IMAGE:figures/full_fig_p052_4_13.png] view at source ↗
Figure 4.14
Figure 4.14. Figure 4.14: Percentages of the EWSR (up to the energy in pare [PITH_FULL_IMAGE:figures/full_fig_p052_4_14.png] view at source ↗
Figure 4.15
Figure 4.15. Figure 4.15: Left side: Electric dipole strength distribut [PITH_FULL_IMAGE:figures/full_fig_p053_4_15.png] view at source ↗
Figure 4.16
Figure 4.16. Figure 4.16: SRPA dipole strength distribution for the [PITH_FULL_IMAGE:figures/full_fig_p054_4_16.png] view at source ↗
Figure 4.17
Figure 4.17. Figure 4.17: For each B(E1) state the N1 contribution to the norm of the state defined in Eq. 4.1 (lower panel) is shown for 48Ca. In the upper panel, the energy in MeV units of some states is reported, for which the corresponding transition densities are shown in [PITH_FULL_IMAGE:figures/full_fig_p055_4_17.png] view at source ↗
Figure 4.18
Figure 4.18. Figure 4.18: Transition densities for 48Ca associated to the different SRPA peaks (see [PITH_FULL_IMAGE:figures/full_fig_p056_4_18.png] view at source ↗
Figure 4.19
Figure 4.19. Figure 4.19: Experimental B(E1) values (panels (a)) from Re [PITH_FULL_IMAGE:figures/full_fig_p056_4_19.png] view at source ↗
Figure 4.20
Figure 4.20. Figure 4.20: Dipole strength distributions for 48Ca obtained in RPA (solid black line), SRPA (blue dotted line), and SSRPA (orange line and area), compared with the experimental distributions (magenta circles) of Ref. [131]. Left side: SGII interaction. Right side: SLy4 interaction. Adapted from Ref. [129]. centroid energies and widths are computed using the following expressions: EC = m1 m0 , ΓC = p m2/m0 − (m1/m0)… view at source ↗
Figure 4.21
Figure 4.21. Figure 4.21: Left side: SSRPA results for 48Ca shifted by 1.5 MeV (green area) compared with the RPA strength (red line) and with the experimental values (blue circles), obtained with the parametrization SGII in panel (a). In panel (b), same results are shown but for the SLy4 case, the shift being in this case of 2.7 MeV. Right side: Electric dipole polarizability as a function of the excitation energy. The area bet… view at source ↗
Figure 4.22
Figure 4.22. Figure 4.22: Left side: SSRPA dipole strength distribution [PITH_FULL_IMAGE:figures/full_fig_p059_4_22.png] view at source ↗
Figure 4.23
Figure 4.23. Figure 4.23: Isovector (a) and isoscalar (b) low–lying stre [PITH_FULL_IMAGE:figures/full_fig_p059_4_23.png] view at source ↗
Figure 4.24
Figure 4.24. Figure 4.24: Transition densities multiplied by r 2 for the peaks located at 9.14 ((a) and (b)), 9.70 ((c) and (d)), 10.25 ((e) and (f)), 11.10 ((g) and (h)), and 11.31 ((i) and (j)) MeV. Neutron and proton transition densities: panels (a), (c), (e), (g), and (i), and isoscalar and isovector transition densities: panels (b), (d), (f), (h), and (j). The used Skyrme parametrization is SGII. Adapted from Ref. [139]. Th… view at source ↗
Figure 4.25
Figure 4.25. Figure 4.25: The cumulative sums of B(M1) strength integrated up to 15 MeV in 48Ca obtained in different measurements compared with the RPA (empty symbols) and SSRPA (filled symbols) with different interactions. The experimental data [148, 149, 150, 151, 152] are shown by the black squares with error bars. Adapted figure from Ref. [145]. interpreted as the orbital scissors mode and it appears mostly in deformed nucl… view at source ↗
Figure 4.26
Figure 4.26. Figure 4.26: Left side: Unperturbed p-h and RPA strength dis [PITH_FULL_IMAGE:figures/full_fig_p062_4_26.png] view at source ↗
Figure 4.27
Figure 4.27. Figure 4.27: Left side: the experimental ISGQR centroids da [PITH_FULL_IMAGE:figures/full_fig_p063_4_27.png] view at source ↗
Figure 4.28
Figure 4.28. Figure 4.28: ISGQR strength distributions obtained in RPA ( [PITH_FULL_IMAGE:figures/full_fig_p063_4_28.png] view at source ↗
Figure 4.29
Figure 4.29. Figure 4.29: As in Figure [PITH_FULL_IMAGE:figures/full_fig_p064_4_29.png] view at source ↗
Figure 4.30
Figure 4.30. Figure 4.30: Strength distributions for 16O using TDA, RSTDA, and RSSTDA with the full form and diagonal approximation (denoted as RSTDA(d) and RSSTD(d), respectively) as a function of excitation energy, for the ISGMR and ISGQR, on the left and right side, respectively. The results for different 2p − 2h energy cutoffs are shown. Adapted from [160]. very high energy cutoffs (Ex ≈ 120 MeV). However, the RSSTDA, despit… view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Left side: Experimental GT− strength in MeV−1 [192] and discrete RPA and SSRPA strength distributions for 48Ca. The RPA strength has been divided by nine and the SSRPA strength by two so that the discrete distributions can be displayed on the same figure as the continuous experimental distribution (see text). The insert shows the energy region between 20 and 30 MeV. Right side: The RPA and SSRPA GT− resp… view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: In panel (d) the experimental percentage of the I [PITH_FULL_IMAGE:figures/full_fig_p068_5_2.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Left side: GT− strengths (panel (a)) obtained for 48Ca in MeV−1 with the Skyrme interaction SGII and cumulative sums (panel (b)). Experimental data are extracted from Ref. [192]. See the text for more details. Adapted from Ref. [141]. Right side: The GT− strength distributions (panel (a)) and corresponding cumulative sums (panel (b)) of 90Zr calculated in SSRPA with SGII force. The red line corresponds t… view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Left side: GT strength distributions for four nu [PITH_FULL_IMAGE:figures/full_fig_p069_5_4.png] view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p070_5_5.png] view at source ↗
Figure 5.6
Figure 5.6. Figure 5.6: GT strength distributions for four nuclei (uppe [PITH_FULL_IMAGE:figures/full_fig_p071_5_6.png] view at source ↗
Figure 5.7
Figure 5.7. Figure 5.7: Cumulative RPA and SSRPA SGT − strengths for 22O (blue) and 14C (green). Horizontal shaded bands indicate the quenched total GT sum rule (SGT − − SGT + ) predicted in Ref.[190] for each nucleus. The vertical dashed magenta line marks an excitation energy of 10 MeV, with the colored vertical bars representing the 70–80% exhaustion of the quenched sum rule up to that energy, as reported in Ref. [190] (see … view at source ↗
Figure 5.8
Figure 5.8. Figure 5.8: (a) Cumulative sum for different models (see lege [PITH_FULL_IMAGE:figures/full_fig_p073_5_8.png] view at source ↗
Figure 5.9
Figure 5.9. Figure 5.9: Experimental β-decay half-lives [201] of 132Sn, 68Ni, 34Si, and 78Ni compared with the RPA (red solid circles) and SSRPA ( blue solid squares) ones. Adapted from Ref. [143] [PITH_FULL_IMAGE:figures/full_fig_p073_5_9.png] view at source ↗
Figure 5.10
Figure 5.10. Figure 5.10: β-decay half-lives of 132Sn, 68Ni, 34Si, and 78Ni calculated using the RPA and SSRPA models with the SAMi-T (left side) and SGII (right side) forces, both with ("w/i-T") and without ("w/o-T") the inclusion of tensor terms, compared to experimental data from Ref. [201]. Experimental values are indicated by black empty circles.Left side: Right side: Figures from Ref. [143] On the left side of [PITH_FULL_… view at source ↗
Figure 5.11
Figure 5.11. Figure 5.11: SGII-SSRPA integrated GT strength in the [PITH_FULL_IMAGE:figures/full_fig_p075_5_11.png] view at source ↗
Figure 5.12
Figure 5.12. Figure 5.12: Experimental β-decay half-lives [201] compared with those obtained within the RPA and SSRPA models. Full (empty) symbols are obtained by using the bare gA = 1.26 (gA = 1.00) constant. The RPA values that are not shown correspond to infinite half-life values. See the text for more details. Adapted from Ref. [144]. These results are consistent with those reported in Ref. [143] and discussed above, with mi… view at source ↗
Figure 5.13
Figure 5.13. Figure 5.13: Comparison between the RPA and SSRPA with and without the J 2 terms. Top panel: the SGII in￾teraction is used. The “*” symbol in the legend indicates that the SGII force has been derived without J 2 terms. Bottom side: The SLy5 interaction is used. The “*” sym￾bol in the legend indicates that the SLy5 force has been derived with J 2 terms. Adapted from Ref. [144]. For the SLy5 force, in the RPA calculat… view at source ↗
Figure 5.14
Figure 5.14. Figure 5.14: Low-lying GT strength distribution obtained i [PITH_FULL_IMAGE:figures/full_fig_p078_5_14.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Left side: EoS for nuclear matter computed using [PITH_FULL_IMAGE:figures/full_fig_p081_6_1.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Left side: Percentage of the pygmy EWSR obtained [PITH_FULL_IMAGE:figures/full_fig_p083_6_2.png] view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Left side: Electric dipole polarizability obta [PITH_FULL_IMAGE:figures/full_fig_p084_6_3.png] view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Left side: RPA Centroid energies of the ISGQRs fo [PITH_FULL_IMAGE:figures/full_fig_p087_6_4.png] view at source ↗
read the original abstract

In this review, we discuss the most recent developments and applications of the Subtracted Second RPA (SSRPA), an extension of the Second RPA (SRPA), which overcomes its pathological issues encountered within the Energy Density Functional theory. After recalling the formal properties of the SRPA and SSRPA, the anomalous behavior of SRPA is shown and discussed by presenting several applications with different kinds of nuclear interactions. The most recent pathology-free SSRPA studies are then presented both for charge-conserving and charge-exchange nuclear excitations. The comparison with experimental data is presented to assess and quantify the improvement introduced by the SSRPA with respect to the RPA and SRPA. The impact of beyond-mean-field correlations induced in SSRPA is also qualitatively estimated in connection with the modeling of the nuclear equation of state. We conclude by discussing the future perspectives of the SSRPA, focusing on its potential connections with some current experimental challenges and outlining necessary theoretical extensions and numerical developments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. This review discusses recent developments and applications of the Subtracted Second RPA (SSRPA) as an extension of the Second RPA (SRPA) that overcomes pathological issues (double-counting, instabilities) within Energy Density Functional theory. It recalls formal properties of SRPA/SSRPA, illustrates SRPA anomalies via applications with different nuclear interactions, presents pathology-free SSRPA results for charge-conserving and charge-exchange excitations, compares these to experimental data to quantify improvements over RPA/SRPA, qualitatively estimates beyond-mean-field correlations' impact on the nuclear equation of state, and outlines future perspectives and needed extensions.

Significance. If the central claims hold, the review offers a timely synthesis of SSRPA's advantages for nuclear response calculations, compiling evidence of improved data agreement and pathology avoidance that could inform modeling of excitations and the EOS. The compilation of charge-conserving and charge-exchange applications provides a useful reference point for the field.

major comments (1)
  1. [Abstract; applications sections on charge-conserving and charge-exchange modes] Abstract and applications sections: the central claim that SSRPA removes SRPA pathologies while exactly preserving physical content requires explicit demonstration that model-independent constraints (energy-weighted sum rules, continuity equation, current conservation) remain satisfied in the numerical results shown for the recent SSRPA studies; the review recalls formal properties but does not report such verifications for the presented applications, leaving open whether reported improvements partly reflect uncontrolled effects of subtraction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract; applications sections on charge-conserving and charge-exchange modes] Abstract and applications sections: the central claim that SSRPA removes SRPA pathologies while exactly preserving physical content requires explicit demonstration that model-independent constraints (energy-weighted sum rules, continuity equation, current conservation) remain satisfied in the numerical results shown for the recent SSRPA studies; the review recalls formal properties but does not report such verifications for the presented applications, leaving open whether reported improvements partly reflect uncontrolled effects of subtraction.

    Authors: The SSRPA method is constructed precisely so that the subtraction removes the double-counting and instability pathologies of SRPA while leaving the physical content unchanged; this guarantees by construction that the energy-weighted sum rules, continuity equation and current conservation are preserved exactly, as already stated in the formal-properties section of the review. The numerical results shown are taken directly from the cited recent SSRPA publications, in which these constraints were verified. To make the review self-contained and remove any possible ambiguity, we will add a short paragraph (or footnote) in the applications sections that explicitly recalls these verifications and points to the checks performed in the original works. This addition will be purely clarificatory and will not alter any of the reported results. revision: yes

Circularity Check

0 steps flagged

Review paper recalling prior formal properties; no new derivations or predictions that reduce to inputs by construction.

full rationale

The manuscript is explicitly a review summarizing existing SSRPA formalism and applications from prior literature. No load-bearing derivation chain is presented in the provided text that equates a claimed result to its own fitted inputs or self-citations by construction. Formal properties are recalled rather than re-derived, and applications are presented as comparisons to data without introducing new self-referential predictions. This matches the default expectation for non-circular reviews.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; all technical content is deferred to cited prior literature.

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