Cross sections of α -induced reactions slightly below doubly magic Ca40 from the statistical model

Mohr, P.; Talwar, R.; Avila, M. L.

doi:10.1103/PhysRevC.98.045805

Title: Cross sections of $α$ -induced reactions slightly below doubly magic ${}^{40}{Ca}$ from the statistical model

Journal Article · 24 October 2018 · Physical Review C

DOI: https://doi.org/10.1103/PhysRevC.98.045805 · OSTI ID:1490333

Mohr, P. ^[1]; Talwar, R. ^[2]; Avila, M. L. ^[2]

Germany and Inst. for Nuclear Research (Atomki), Debrecen (Hungary)
Argonne National Lab. (ANL), Argonne, IL (United States). Physics Division

New experimental data for the ³⁸Ar (α , n) ⁴¹Ca and ³⁸Ar (α, p) ⁴¹K reactions were used to find a best-fit set of parameters for statistical model calculations. The very good agreement between the experimental data and the best-fit calculation confirms the applicability of the statistical model for nuclei in the vicinity of the doubly magic ⁴⁰Ca despite their relatively low level densities. The present study investigates the sensitivities and finds that the α -nucleus and the nucleon-nucleus potentials are the most important ingredients for the calculation of (α, n) and (α, p) reactions in the statistical model. Furthermore, the width fluctuation correction plays an essential role in the peculiar case of ³⁸Ar. The best-fit parameters from ³⁸Ar are applied to the mirror nucleus ³⁸Ca and the neighboring ³⁶Ar and ⁴⁰Ar nuclei. For ³⁸Ca this results in an astrophysical reaction rate of the 38 Ca (α , p) ⁴¹Sc reaction, which has a flatter temperature dependence compared to all previous calculations. For ⁴⁰Ar a better reproduction of ⁴⁰Ar (α , p) ⁴³K data from literature is obtained. The disagreement between calculation and an early experimental data point for the ³⁶Ar (α, p) ³⁹K reaction persists.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Research Development and Innovation Office of Hungary (NKFIH); USDOE; USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1490333

Journal Information:: Physical Review C, Journal Name: Physical Review C Journal Issue: 4 Vol. 98; ISSN PRVCAN; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (52)

Astrophysical Reaction Rates From Statistical Model Calculations Rauscher, Thomas; Thielemann, Friedrich-Karl Atomic Data and Nuclear Data Tables, Vol. 75, Issue 1-2 https://doi.org/10.1006/adnd.2000.0834	journal	May 2000
A Hartree–Fock Nuclear mass Table Goriely, S.; Tondeur, F.; Pearson, J. M. Atomic Data and Nuclear Data Tables, Vol. 77, Issue 2 https://doi.org/10.1006/adnd.2000.0857	journal	March 2001
Direct reactions and Hauser-Feshbach theory Hofmann, H. M.; Richert, J.; Tepel, J. W. Annals of Physics, Vol. 90, Issue 2 https://doi.org/10.1016/0003-4916(75)90005-6	journal	April 1975
High energy scattering of deuterons by complex nuclei Watanabe, Shigueo Nuclear Physics, Vol. 8 https://doi.org/10.1016/0029-5582(58)90180-9	journal	September 1958
Optical-model analysis of the scattering of 24.7 MeV alpha particles McFadden, Lynne; Satchler, G. R. Nuclear Physics, Vol. 84, Issue 1 https://doi.org/10.1016/0029-5582(66)90441-X	journal	August 1966
Grassmann integration in stochastic quantum physics: The case of compound-nucleus scattering Verbaarschot, J. J. M.; Weidenmüller, H. A.; Zirnbauer, M. R. Physics Reports, Vol. 129, Issue 6 https://doi.org/10.1016/0370-1573(85)90070-5	journal	December 1985
Level density parameters for the back-shifted fermi gas model in the mass range 40 < A < 250 Dilg, W.; Schantl, W.; Vonach, H. Nuclear Physics A, Vol. 217, Issue 2 https://doi.org/10.1016/0375-9474(73)90196-6	journal	December 1973
Excitation function and thick target yield of the 40Ar(α,p)43K reaction: Production of 43K Fenyvesi, A.; Tárkányi, F.; Szelecsényi, F. Applied Radiation and Isotopes, Vol. 46, Issue 12 https://doi.org/10.1016/0969-8043(95)00217-2	journal	December 1995
Comparisons between various width fluctuation correction factors for compound nucleus reactions Hilaire, S.; Lagrange, Ch.; Koning, A. J. Annals of Physics, Vol. 306, Issue 2 https://doi.org/10.1016/S0003-4916(03)00076-9	journal	August 2003
Capture of particles by isospin-symmetric nuclei Rauscher, T.; Thielemann, F. -K.; Görres, J. Nuclear Physics A, Vol. 675, Issue 3-4 https://doi.org/10.1016/S0375-9474(00)00182-2	journal	August 2000
Improved global α-optical model potentials at low energies Demetriou, P.; Grama, C.; Goriely, S. Nuclear Physics A, Vol. 707, Issue 1-2 https://doi.org/10.1016/S0375-9474(02)00756-X	journal	August 2002
Local and global nucleon optical models from 1 keV to 200 MeV Koning, A. J.; Delaroche, J. P. Nuclear Physics A, Vol. 713, Issue 3-4 https://doi.org/10.1016/S0375-9474(02)01321-0	journal	January 2003
Elastic alpha scattering experiments and the alpha-nucleus optical potential at low energies Mohr, P.; Kiss, G. G.; Fülöp, Zs. Atomic Data and Nuclear Data Tables, Vol. 99, Issue 6 https://doi.org/10.1016/j.adt.2012.10.003	journal	November 2013
Nuclear Data Sheets for A = 41 Nesaraja, C. D.; McCutchan, E. A. Nuclear Data Sheets, Vol. 133 https://doi.org/10.1016/j.nds.2016.02.001	journal	March 2016
X-ray binaries Schatz, H.; Rehm, K. E. Nuclear Physics A, Vol. 777 https://doi.org/10.1016/j.nuclphysa.2005.05.200	journal	October 2006
The isovector imaginary neutron potential: A key ingredient for the r-process nucleosynthesis Goriely, S.; Delaroche, J. -P. Physics Letters B, Vol. 653, Issue 2-4 https://doi.org/10.1016/j.physletb.2007.07.046	journal	September 2007
Nucleosynthesis in type I X-ray bursts Parikh, A.; José, J.; Sala, G. Progress in Particle and Nuclear Physics, Vol. 69 https://doi.org/10.1016/j.ppnp.2012.11.002	journal	March 2013
Explosive hydrogen burning Wallace, R. K.; Woosley, S. E. The Astrophysical Journal Supplement Series, Vol. 45 https://doi.org/10.1086/190717	journal	January 1981
The jina Reaclib Database: its Recent Updates and Impact on Type-I X-Ray Bursts Cyburt, Richard H.; Amthor, A. Matthew; Ferguson, Ryan The Astrophysical Journal Supplement Series, Vol. 189, Issue 1 https://doi.org/10.1088/0067-0049/189/1/240	journal	June 2010
Sensitivity of Astrophysical Reaction Rates to Nuclear Uncertainties Rauscher, T. The Astrophysical Journal Supplement Series, Vol. 201, Issue 2 https://doi.org/10.1088/0067-0049/201/2/26	journal	July 2012
Starlib: a Next-Generation Reaction-Rate Library for Nuclear Astrophysics Sallaska, A. L.; Iliadis, C.; Champange, A. E. The Astrophysical Journal Supplement Series, Vol. 207, Issue 1 https://doi.org/10.1088/0067-0049/207/1/18	journal	July 2013
Alpha-Particle Bombardment of A 36 and A 40 Schwartz, R. B.; Corbett, J. W.; Watson, W. W. Physical Review, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRev.101.1370	journal	February 1956
The Inelastic Scattering of Neutrons Hauser, Walter; Feshbach, Herman Physical Review, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRev.87.366	journal	July 1952
Evaluation of the fluctuation enhancement factor Moldauer, P. A. Physical Review C, Vol. 14, Issue 2 https://doi.org/10.1103/PhysRevC.14.764	journal	August 1976
Optical-model potential in finite nuclei from Reid's hard core interaction Jeukenne, J. -P.; Lejeune, A.; Mahaux, C. Physical Review C, Vol. 16, Issue 1 https://doi.org/10.1103/PhysRevC.16.80	journal	July 1977
Global optical potential for α particles with energies above 80 MeV Nolte, M.; Machner, H.; Bojowald, J. Physical Review C, Vol. 36, Issue 4 https://doi.org/10.1103/PhysRevC.36.1312	journal	October 1987
Role of isospin in neutron- and alpha-induced reactions Grimes, S. M. Physical Review C, Vol. 46, Issue 3 https://doi.org/10.1103/PhysRevC.46.1064	journal	September 1992
Density of discrete levels in Sn 116 Ignatyuk, A. V.; Weil, J. L.; Raman, S. Physical Review C, Vol. 47, Issue 4 https://doi.org/10.1103/PhysRevC.47.1504	journal	April 1993
Global optical potentials for emitted alpha particles Avrigeanu, V.; Hodgson, P. E.; Avrigeanu, M. Physical Review C, Vol. 49, Issue 4 https://doi.org/10.1103/PhysRevC.49.2136	journal	April 1994
Lane-consistent, semimicroscopic nucleon-nucleus optical model Bauge, E.; Delaroche, J. P.; Girod, M. Physical Review C, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevC.63.024607	journal	January 2001
Improved microscopic nuclear level densities within the Hartree-Fock-Bogoliubov plus combinatorial method Goriely, S.; Hilaire, S.; Koning, A. J. Physical Review C, Vol. 78, Issue 6 https://doi.org/10.1103/PhysRevC.78.064307	journal	December 2008
Temperature-dependent combinatorial level densities with the D1M Gogny force Hilaire, S.; Girod, M.; Goriely, S. Physical Review C, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevC.86.064317	journal	December 2012
Total reaction cross section σ reac of α -induced reactions from elastic scattering: The example 140 Ce( α , α ) 140 Ce Mohr, Peter Physical Review C, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevC.87.035802	journal	March 2013
Measurement of the 33 S( α , p ) 36 Cl cross section: Implications for production of 36 Cl in the early Solar System Bowers, M.; Kashiv, Y.; Bauder, W. Physical Review C, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevC.88.065802	journal	December 2013
Unexpected properties of the 33 S ( α , p ) 36 Cl reaction cross section at low energies Mohr, Peter Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.058801	journal	May 2014
Further explorations of the α -particle optical model potential at low energies for the mass range A ≈ 45 –209 Avrigeanu, V.; Avrigeanu, M.; Mănăilescu, C. Physical Review C, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevC.90.044612	journal	October 2014
Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies Kawano, T.; Capote, R.; Hilaire, S. Physical Review C, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevC.94.014612	journal	July 2016
Experimental study of the astrophysically important Na 23 ( α , p ) Mg 26 and Na 23 ( α , n ) Al 26 reactions Avila, M. L.; Rehm, K. E.; Almaraz-Calderon, S. Physical Review C, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRevC.94.065804	journal	December 2016
Statistical model analysis of α -induced reaction cross sections of Zn 64 at low energies Mohr, P.; Gyürky, Gy.; Fülöp, Zs. Physical Review C, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevC.95.015807	journal	January 2017
Indirect study of the stellar Ar 34 ( α , p ) K 37 reaction rate through Ca 40 ( p , t ) Ca 38 reaction measurements Long, A. M.; Adachi, T.; Beard, M. Physical Review C, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevC.95.055803	journal	May 2017
Re-measurement of the S 33 ( α , p ) Cl 36 cross section for early solar system nuclide enrichment Anderson, Tyler; Skulski, Michael; Clark, Adam Physical Review C, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevC.96.015803	journal	July 2017
First measurement of S 30 + α resonant elastic scattering for the S 30 ( α , p ) reaction rate Kahl, D.; Yamaguchi, H.; Kubono, S. Physical Review C, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevC.97.015802	journal	January 2018
α -unbound levels in Ar 34 from Ar 36 ( p , t ) Ar 34 reaction measurements and implications for the astrophysical S 30 ( α , p ) Cl 33 reaction rate Long, A. M.; Adachi, T.; Beard, M. Physical Review C, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevC.97.054613	journal	May 2018
Experimental study of Ar 38 + α reaction cross sections relevant to the Ca 41 abundance in the solar system Talwar, R.; Bojazi, M. J.; Mohr, P. Physical Review C, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevC.97.055801	journal	May 2018
Direct Measurement of the Na 23 ( α , p ) Mg 26 Reaction Cross Section at Energies Relevant for the Production of Galactic Al 26 Almaraz-Calderon, S.; Bertone, P. F.; Alcorta, M. Physical Review Letters, Vol. 112, Issue 15 https://doi.org/10.1103/PhysRevLett.112.152701	journal	April 2014
Na 23 ( α , p ) Mg 26 Reaction Rate at Astrophysically Relevant Energies Howard, A. M.; Munch, M.; Fynbo, H. O. U. Physical Review Letters, Vol. 115, Issue 5 https://doi.org/10.1103/PhysRevLett.115.052701	journal	July 2015
Measurement of Na 23 ( α , p ) Mg 26 at Energies Relevant to Al 26 Production in Massive Stars Tomlinson, J. R.; Fallis, J.; Laird, A. M. Physical Review Letters, Vol. 115, Issue 5 https://doi.org/10.1103/PhysRevLett.115.052702	journal	July 2015
Erratum: Direct Measurement of the Na 23 ( α , p ) Mg 26 Reaction Cross Section at Energies Relevant for the Production of Galactic Al 26 [Phys. Rev. Lett. 112 , 152701 (2014)] Almaraz-Calderon, S.; Bertone, P. F.; Alcorta, M. Physical Review Letters, Vol. 115, Issue 17 https://doi.org/10.1103/PhysRevLett.115.179901	journal	October 2015
A Composite Nuclear-Level Density Formula with Shell Corrections Gilbert, A.; Cameron, A. G. W. Canadian Journal of Physics, Vol. 43, Issue 8 https://doi.org/10.1139/p65-139	journal	August 1965
Cross sections of α-induced reactions for targets with masses A ≈ 20–50 at low energies Mohr, Peter The European Physical Journal A, Vol. 51, Issue 5 https://doi.org/10.1140/epja/i2015-15056-5	journal	May 2015
The path to Improved Reaction Rates for Astrophysics Rauscher, Thomas International Journal of Modern Physics E, Vol. 20, Issue 05 https://doi.org/10.1142/S021830131101840X	journal	May 2011
Reactions of Argon-40 with Alpha-Particles Tanaka, Shigeo; Furukawa, Michiaki; Mikumo, Takashi Journal of the Physical Society of Japan, Vol. 15, Issue 6 https://doi.org/10.1143/JPSJ.15.952	journal	June 1960

Cited By (2)

Cross section of α -induced reactions on Au 197 at sub-Coulomb energies Szücs, T.; Mohr, P.; Gyürky, Gy. Physical Review C, Vol. 100, Issue 6 https://doi.org/10.1103/physrevc.100.065803	journal	December 2019
Cross-sections at sub-Coulomb energies: Full optical model versus barrier transmission for 40Ca + α Mohr, Peter International Journal of Modern Physics E, Vol. 28, Issue 05 https://doi.org/10.1142/s0218301319500290	journal	May 2019