A reliable determination of the pole parameters and residues of nucleon resonances is notoriously challenging, given the required analytic continuation into the complex plane. We provide a comprehensive analysis of such resonance parameters accessible with Roy–Steiner equations for pion–nucleon scattering—a set of partial-wave dispersion relations that combines the constraints from analyticity, unitarity, and crossing symmetry—most prominently of the <math><mi>Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo></math> resonance. Further, we study the Roper, <math><mi>N</mi><mo>(</mo><mn>1440</mn><mo>)</mo></math>, resonance, which lies beyond the strict domain of validity, in comparison to Padé approximants, comment on the role of subthreshold singularities in the S-wave, and determine the residues of the <math><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>500</mn><mo>)</mo></math>, <math><mi>ρ</mi><mo>(</mo><mn>770</mn><mo>)</mo></math>, and <math><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> resonances in the t-channel process <math><mi>π</mi><mi>π</mi><mo>→</mo><mover><mrow><mi>N</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>N</mi></math>. The latter allows us to test—for the first time fully model independently in terms of the respective residues—universality of the <math><mi>ρ</mi><mo>(</mo><mn>770</mn><mo>)</mo></math> couplings and the Goldberger–Treiman relation expected if the scalars behaved as dilatons, in both cases revealing large deviations from the narrow-resonance limit.

Switzerland

Martin Hoferichter

Spain

Jacobo Ruiz de Elvira

Germany

Bastian Kubis

Ulf-G. Meißner

Nucleon resonance parameters from Roy–Steiner equations

An extended Roy equation including a bound state pole is used to study <math><mi>π</mi><mi>π</mi></math> scatterings at unphysical large pion masses when <math><mi>σ</mi></math> becomes a bound state in one situation and stays as a broad resonance in the other case. The coupled integral equations at large pion masses are solved by taking the lattice driving terms and the Regge amplitudes as inputs. Relying on the solutions of Roy equations that respect unitarity, analyticity and crossing symmetry, we give predictions to the phase shifts with <math><mi>I</mi><mi>J</mi><mo>=</mo><mn>00</mn></math>, 11, 20 in the elastic energy region. We then perform analytic continuation into the complex <math><mi>s</mi></math> plane to search for various poles, all of which are inside the validity domain of the Roy equation. This is the first time that lattice data at unphysical large pion masses are analyzed within the rigorous Roy equation method.

China

Xiong-Hui Cao

Qu-Zhi Li

Zhi-Hui Guo

Han-Qing Zheng

Roy equation analyses of <math><mi>π</mi><mi>π</mi></math> scatterings at unphysical pion masses

The hyperbolic version of Roy-Steiner equation describing low energy πN scatterings, with larger analyticity domain in the complex s plane is solved. The numerical results on phase shifts of low partial waves are in agreement with that of Hoferichter et al. [Phys. Rept. 625 (2016) 1]. A subthreshold pole in S 11 channel is found located at   <math> <msqrt> <mi>s</mi> </msqrt> </math>  $$ \sqrt{s} $$  = (918 ± 3) − i(163 ± 9) MeV.

A possible subthreshold pole in S 11 channel from πN Roy-Steiner equation analyses

Evaporated α-spectra have been measured in coincidence with low energy discrete γ-rays from residual nucleus $^{68}$Zn populated by αn evaporation from compound nucleus $^{73}$Ge produced in the reaction $^{64}$Ni($^{9}$Be,αn)$^{68}$Zn at <math><mi>E</mi><mo>(</mo><msup><mrow></mrow><mrow><mn>9</mn></mrow></msup></math>Be) = 30 MeV. Low energy γ-gated α-particle spectra, for the first time, have been used to extract the nuclear level density (NLD) for the intermediate $^{69}$Zn nucleus in the excitation energy range of E ≈ 4-20 MeV. The slope of present NLD data as a function of excitation energy for $^{69}$Zn matches nicely with the slope determined from RIPL estimates for NLD at low energies and the NLD from neutron resonance data at neutron separation energy <math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math>. The extracted inverse NLD parameter (k = A/<math><mover><mrow><mi>a</mi></mrow><mrow><mo>˜</mo></mrow></mover></math>) has been used to determine the nuclear level density parameter value a at neutron separation energy <math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math> for $^{69}$Zn. The cross section of $^{68}$Zn(n,γ) capture reaction as a function of neutron energy is then estimated employing the derived <math><mi>a</mi><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math> in the reaction code TALYS. It is found that the estimated neutron capture cross section agrees well with the available experimental data without any normalization. The present result indicates that experimentally derived nuclear level density parameter can constrain the statistical model description of astrophysical capture cross section and optimize the uncertainties associated with astrophysical reaction rate.

India

Rajkumar Santra

Balaram Dey

Subinit Roy

Md.S.R. Laskar

R. Palit

H. Pai

S. Rajbanshi

Sajad Ali

Saikat Bhattacharjee

F.S. Babra

Anjali Mukherjee

S. Jadhav

Balaji S. Naidu

Abraham T. Vazhappilly

Sanjoy Pal

Nuclear level density of Zn from gamma gated particle spectrum and its implication on Zn(n, ) Zn capture cross section