Low-lying level structure of {}^{56}Cu and its implications on the rp process

Low-lying level structure of Cu and its implications on the rp process

W-J. Ong National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    C. Langer National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA    F. Montes National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA    A. Aprahamian Department of Physics and Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA    D. W. Bardayan [ Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    D. Bazin National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA    B. A. Brown National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    J. Browne National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    H. Crawford Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley CA, 94720, USA    R. Cyburt National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA    E. B. Deleeuw National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    C. Domingo-Pardo IFIC, CSIC-University of Valencia, E-46071 Valencia, Spain    A. Gade National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    S. George Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany Institut f. Physik, Ernst-Moritz-Arndt-Universität, 17487 Greifswald, Germany    P. Hosmer Department of Physics, Hillsdale College, Hillsdale, MI 49242, USA    L. Keek National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    A. Kontos National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA    I-Y. Lee Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley CA, 94720, USA    A. Lemasson National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA    E. Lunderberg National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    Y. Maeda Department of Applied Physics, University of Miyazaki, Miyazaki, Miyazaki 889-2192, Japan    M. Matos Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA    Z. Meisel National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    S. Noji National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA    F. M. Nunes National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    A. Nystrom Department of Physics and Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA    G. Perdikakis Department of Physics, Central Michigan University, Mt. Pleasant, MI 48859, USA National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA    J. Pereira National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA    S. J. Quinn National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    F. Recchia National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA    H. Schatz National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    M. Scott National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    K. Siegl Department of Physics and Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA    A. Simon Gottwald Center for the Sciences, University of Richmond, 28 Westhampton Way, Richmond, VA 23173 National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA    M. Smith Department of Physics and Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA    A. Spyrou National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    J. Stevens National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    S. R. Stroberg National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    D. Weisshaar National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA    J. Wheeler National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA    K. Wimmer Department of Physics, Central Michigan University, Mt. Pleasant, MI 48859, USA National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA    R. G. T. Zegers National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
July 24, 2019
Abstract

The low-lying energy levels of proton-rich Cu have been extracted using in-beam -ray spectroscopy with the state-of-the-art -ray tracking array GRETINA in conjunction with the S800 spectrograph at the National Superconducting Cyclotron Laboratory at Michigan State University. Excited states in Cu serve as resonances in the Ni(p,)Cu reaction, which is a part of the rp-process in type I x-ray bursts. To resolve existing ambiguities in the reaction Q-value, a more localized IMME mass fit is used resulting in  keV. We derive the first experimentally-constrained thermonuclear reaction rate for Ni(p,)Cu. We find that, with this new rate, the rp-process may bypass the Ni waiting point via the Ni(p,) reaction for typical x-ray burst conditions with a branching of up to 40. We also identify additional nuclear physics uncertainties that need to be addressed before drawing final conclusions about the rp-process reaction flow in the Ni region.

pacs:
29.30.Kv, 07.85.Nc, 26.30.Ca, 25.40.Lw, 25.60.Je, 23.20.Lv
preprint: APS/123

Present address: ]Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA

I Introduction

Accreting neutron stars in binary systems undergo episodes of explosive hydrogen and helium burning, observed as Type-I x-ray bursts. The main observable of these events, the x-ray burst light-curve, is shaped by the nuclear energy generation during the rapid proton-capture process (rp-process) Wallace and Woosley (1981); Schatz et al. (1998). This process involves a series of proton captures and -decays that proceed near the proton-drip line.

Reaction rates connected to the so-called waiting point nuclei van Wormer et al. (1994), where the reaction flow slows down significantly, have the most significant impact on the observed light curve. The doubly-magic nucleus Ni has been identified as one of a few major waiting points in the rp-process. This is due to the combination of its long stellar electron capture half-life of 3 hrs Fuller et al. (1982) (which for the fully ionized ion differs from its terrestrial half-life and depends on the stellar electron density), and its low proton-capture Q-value (690 keV) Audi et al. (2014). The effective lifetime of Ni under typical x-ray burst conditions, which depends steeply on temperature, has been constrained by experimental data related to the Ni(p,) Rehm et al. (1998); Forstner et al. (2001) and Cu(p,) Langer et al. (2014) reaction rates. However, large uncertainties exist in the nuclear physics of more neutron-deficient nuclei in the Ni region. In particular, a sequence of proton-capture reactions in the Ni, Cu, Zn isotonic chain may be strong enough for the rp-process to bypass Ni (Fig. 1). In this case, Ni would not be an rp-process waiting point, reducing the sensitivity of burst models to the Ni(p,) rate. The Cu(p,) reaction rate remains important because the bypass exits the N=27 isotonic chain through -decay of Zn to Cu. Consequently, the reaction flow would proceed more rapidly into the Ge-Se-Kr mass region and a lower amount of A = 56 material would be produced in the ashes.

Figure 1: The nuclide chart in the region of the Ni waiting point. The conventional -process flow leading to Ni is denoted by the solid line. The potential bypass, sequential proton-captures along the N = 27 isotonic chain, is denoted by the dashed line.

The Ni(p,) reaction determines the branching at Ni into the Ni bypass reaction sequence. Here, we address uncertainties in this reaction rate experimentally, and reanalyze theoretical predictions of the reaction Q-value. We then use the new data to determine, in the context of the remaining nuclear physics uncertainties, the conditions under which the rp-process bypasses Ni.

The Ni(p,)Cu reaction proceeds through a few isolated narrow resonances, and the astrophysical rate can be approximated by

(1)

where is the resonance energy with reaction Q-value and Cu exitation energy . The resonance strength is given by

(2)

Here, is the resonance spin, the proton spin, is the ground-sate spin of Ni, the proton partial width, the partial width and .

Only scarce experimental data for the odd-odd Cu nucleus exist in the literature. Cu, as well as its well-understood mirror nucleus Co, are part of the , isospin triplet. Based on this, the ground-state of Cu is assumed to be with a measured terrestrial -decay half-life of 93(3) ms Junde et al. (2011). To date, no low-lying excited states have been observed experimentally. In a recent -delayed proton decay study of Zn, several higher-lying Cu resonances above 1391 keV excitation energy were observed Orrigo et al. (2014). Under astrophysical conditions, however, these resonances are too high in energy to be of relevance. In the absence of knowledge of spectroscopic information, shell-model calculations using the KB3 interaction in the -shell performed with the code ANTOINE have been used in the past Fisker et al. (2001). However, uncertainties in shell-model predictions of excitation energies can amount up to 200 keV, leading to orders of magnitude uncertainty in the resonant-capture rate. Here we experimentally determine, for the first time, the excitation energies of low-lying states in Cu that serve as resonances in the Ni(p,)Cu reaction

For a precise determination of the Ni(p,)Cu rate, both the low-lying level scheme of Cu and the reaction Q-value need to be well-known since the resonance energies enter the rate exponentially. While the mass of Ni is experimentally well-known with an error of 0.75 keV Kankainen et al. (2010), the mass of Cu is not experimentally known. Conflicting predictions for the Cu mass exist in the literature. The extrapolated Cu mass in the AME2003 compilation Wapstra et al. (2003) results in a Ni proton-capture Q-value of 560(140) keV. A similar result of 600(100) keV is obtained with Coulomb shift calculations Brown et al. (2002). Using the Cu mass in the most recent AME2012 compilation, however, results in a Q-value of 190(200) keV Audi et al. (2014). We obtain a new prediction for the reaction Q-value by using the isobaric multiplet mass equation (IMME).

Ii Experimental Determination of the Cu level scheme

Excited states of Cu were populated in inverse kinematics in an experiment performed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University Langer et al. (2014). A stable 160 MeV/ Ni primary beam impinged on a 752 mg/cm Be target placed at the entrance of the A1900 fragment separator Morrissey et al. (2003). After purification by the A1900 using the method, the produced Ni secondary beam had a rate of  pps with a beam purity of . The Ni beam (E =  MeV/u) was then incident upon a 225 mg/cm CD target, producing Cu through various reaction channels. The CD target was located in the center of the -ray energy tracking array GRETINA Paschalis et al. (2013), which was used to measure energies of the prompt -rays emitted from the de-excitation of the excited states in Cu. GRETINA consists of 28 coaxial HPGe detector crystals, which are closely-packed to cover roughly 1 in solid angle. Kinematical reconstruction of the momentum, angle, and position of each Cu recoil at the target based on observables at the S800 focal plane, combined with the high position resolution for -ray detection in GRETINA allow for accurate Doppler-shift corrections for -rays emitted in-flight. The recoil velocity used for the Doppler-shift correction was extracted using momentum information, and was determined for each individual event to correct for energy loss in the target. The Cu recoils, after leaving the target, were identified using detectors situated in the focal plane of the S800 spectrograph Bazin et al. (2003) located downstream from GRETINA. The S800 focal plane contained a set of two cathode readout drift counters that were used to determine the particle trajectory, a gas-filled ionization chamber that measured energy loss , and a plastic scintillator that, along with the thin timing scintillator at the A1900 focal plane and the scintillator at the S800 object position, were used for time-of-flight (TOF) analysis. The measured time-of-flight between the A1900 focal plane and S800 object scintillators was used to uniquely identify the Cu recoil by -TOF (Fig. 2).

Figure 2: (Color online:) -TOF particle identification for ions reaching the S800 focal plane. Color indicates the number of counts per bin. The Ni isotopic chain (dotted line) and the Ni (leftmost ellipse), Cu (rightmost ellipse), and Cu (middle ellipse) isotopes are also marked (not actual analysis gates).

The low-lying level scheme of Cu was constructed using observed -ray transitions, coincidences and guidance from the experimentally based level scheme of the mirror nucleus Co. The Doppler-corrected spectrum of the -rays detected by GRETINA, in coincidence with the Cu recoils in the S800, shows five -ray transitions (Fig. 3). An additional line at  = 1027 keV stems from contamination from a well-known -ray transition in Cu which is located next to Cu in the particle identification spectrum (Fig. 2). We confirmed that this -ray line disappears from the spectrum when the particle identification gate in Fig. 2 is tightened to only include the most centrally located events in the Cu recoil region.

Figure 3: Doppler-corrected -ray spectrum measured with GRETINA in coincidence with Cu ions in the S800 focal plane. A nearest neighbor addback algorithm has been applied. The asterisk indicates contamination from Cu.

The left half of figure 5 shows the reconstructed Cu level scheme. The strongest observed line at  = 166(1) keV is close in energy to the first excited state at 158 keV () in the mirror nucleus Co. Based on experimental information from the Co mirror nucleus, we expect the first excited state to be the most intense transition as it is fed from several higher-lying states. This line is observed to be in coincidence with two other -transitions, supporting its assignment as direct decay from the the first excited state (Fig. 4).

The transitions at  = 660(3) keV and  = 871(3) keV are observed to be in coincidence with the  = 166(1) keV transition as shown in Fig. 4, but not with each other. Based on the prior assignment of the 166 keV first excited state, two states are placed at  keV and  keV, respectively. No ground state decays are observed for either of these states. There are three known states in the Co mirror at similar energies of and  keV. Of those, the 1009 keV state decays predominantly to the ground state. Both the 830 keV and 970 keV states decay primarily to the first excited state at 158 keV with only a 34 and 0.3 direct transition to the ground state, respectively. Based on the decay modes and similarities in energies, the two observed states at  keV and  keV are tentatively assigned as and , respectively.

The observed line at  = 572(1) keV is not seen in coincidence with the 166 keV line. The mirror Co has a state at  keV that decays only to the ground state. Based on the similar energies and similar decay modes, we tentatively assign the 572 keV transition to be the second excited state.

The  keV line is not observed to be in coincidence with any other -ray transition, and it is therefore assigned to a level at that energy. The analog states in the mirror with the closest energies are 1009 keV () and 1115 keV () which both decay largely to the ground state. Other higher lying states in Co (the next one is at 1450 keV) decay predominantly through cascades, which is not supported by our measurement. We tentatively assign  keV as either the  = 3 or the state. The observed transitions, intensities and assignments are tabulated in Table 1. A comparison to the mirror nucleus is shown in Fig. 5.

Figure 4: coincidences with = 871 (3) keV (upper panel) and = 660 (3) keV (lower panel).
Figure 5: (Color online:) Proposed low-lying level scheme of Cu (left) in comparison to its mirror nucleus Co (right). Tentative spin and parity assignments are shown in parentheses. The observed -transitions are shown, with the corresponding transitions in the mirror shown with the same color.
(keV) (keV) ()
166 (1) 166 (1) 100
572 (1) 572 (1) 122 (8)
826 (3) 660 (3) 28 (8)
1037 (3) 871 (3) 50 (8)
1224 (4) 1224 (4) 19 (10)
Table 1: Reconstructed level scheme of Cu excitation levels with observed transition energies (), relative intensities () normalized to the  = 166 keV line, and tentative spin-parity assignments (see text for details).

Iii Mass Estimate of Cu using the Isobaric Multiplet Mass Equation

We use the isobaric mass multiplet equation (IMME) to predict a new Cu mass, which is needed to derive the reaction Q-value and the resonance energies. The Cu ground state (J) is part of the , triplet, and its mass excess can be calculated using

(3)

The coefficient for integer triplets is the mass excess of the isobaric analogue state (IAS) of the  = 0 member of the triplet, in this case the state in Ni, and can be calculated from the reported IAS excitation energy of 6432 keV Borcea et al. (2001). The IMME and coefficients for the triplet have not been published, but can be estimated using fits to coefficients of triplets in the vicinity of . Global fit functions of IMME parameters have been discussed in MacCormick and Audi (2014), where the authors treat the nucleus as a homogeneous charged sphere, and coefficients , and are reported for the subgroups. Here, we fit only to coefficients for a local region with A32, 36, 40 and 48. As per the homogeneous charged sphere approximation of Jänecke (1966), the and coefficients can be parametrized in the following manner:

(4)
(5)

where are fit parameters. The fits obtained for and in the local vicinity are then used for the , subgroup. The resulting fit extrapolated to results in = 110(95) keV and = -8680(109) keV. Along with the result for the coefficient from Borcea et al. (2001) of 6431.9 (7)   keV, this provides a mass excess prediction for Cu of -38685(82) keV and, thus, a Q-value of 639 82 keV. The error is taken from the largest deviation between a measured mass and the predicted value from the fit function in the local region of interest.

Q-value (keV) Method Reference
560 140 Mass extrapolation AME2003 Wapstra et al. (2003)
190 200 Mass extrapolation AME2012 Audi et al. (2014)
600 100 Coulomb Shift / Shell Model Brown et al. Brown et al. (2002)
639 82 IMME This work
Table 2: Summary of predictions for the Q-value of Ni.

As seen in Table 2, the more precise estimate from this work agrees within errors with the Coulomb-shift calculation from Brown et al. (2002), favoring a higher Q-value compared to the lower extrapolated value reported in the AME2012 compilation. A recent IMME-based estimate using the T=2 quintet Tu et al. (2016) reported a Q-value of 651(88) keV. Moreover, requiring reasonable Coulomb shifts for higher-lying mirror states, as extracted experimentally in Orrigo et al. (2014) between Cu and Co, also favors a higher Q-value.

Iv Thermonuclear reaction rate

With our measurement and our predicted Cu mass, we have determined the resonance energies of the Ni(p,)Cu reaction. In order to determine the astrophysical reaction rate, proton- and -widths ( and respectively) were calculated for each state using a shell-model with the GXPF1A interaction Honma et al. (2005) (Table LABEL:table1). These calculations allowed up to 3-particle 3-hole excitations in the -shell.

Experiment Shell Model
(keV) (keV) (keV) (keV) (eV) (eV)
166(1) 146
572(1) 483 0.70 0.16
826(3) 187(82) 1066 427 0.12 0.69
1037(3) 398(82) 1023 384 0.64 0.16
1224(4) 585(82)
1146
1474
507
835
0.15
0.10
0.71
0.68
1582 943
1913 1274 0.57
2036 1397
2066 1427 0.59 48
2226 1587 0.53
2272 1633 0.63 0.13 210
2350 1711
2393 1754 0.72 5.5
2419 1780
2483 1844 59
2505 1866 0.11
2543 1904 23
2630 1991 19
2723 2084 75
2762 2123 2.6
2914 2275 77
Table 3: New measured and shell-model excitation energies for Cu up to 3 MeV, resonance energies (), and tentative spin-parity assignments. Spectroscopic factors used to calculate the partial proton and gamma widths ( and respectively) were calculated utilizing a shell model calculation with the GXPF1A interaction, using experimental energies when available.

Reaction-rate uncertainties were calculated with a Monte-Carlo approach, similar to that of Iliadis et al. (2015), to properly account for the uncertainties in the excitation energies. Resonance energies and the reaction Q-value were allowed to vary assuming a Gaussian distribution within the uncertainties given in Table LABEL:table1. The uncertainty in the spin assignment for the 1224 keV state was also taken into account, but this represented only a small percentage of the uncertainty. The sampled resonance energy and corresponding rescaled proton-widths are used as input to Eq. 1, producing a sample of rates. At a given temperature, the 50, 16 and 84 percentiles of the distribution of rate values provides the median, and 1- uncertainty, respectively. The results are shown in Fig. 6. To assess the reaction rate uncertainty prior to our measurement, we used the shell-model calculation and assumed a 200 keV uncertainty for the resonance energies. The resulting rate uncertainty (the light blue band in Fig. 6) ranges from 4 orders of magnitude at 0.1 GK to about an order of magnitude at 2.0 GK. This is reduced at low temperatures to less than two orders of magnitude by our measurement (the gray band in Fig. 6). The additional uncertainty from the calculated proton and partial widths is estimated to be significantly smaller, about of a factor of 2 Langer et al. (2014). Thus, the dominant remaining source of uncertainty is the 80 keV error in the Cu mass, with smaller contributions from the uncertainties of the experimentally-unmeasured proton and partial widths.

Table LABEL:reaclibtab gives the corresponding REACLIB rate fit coefficients, using the parametrization given in Eqn. 6, for our updated Ni(p,) reaction rate.

(6)
Figure 6: (Color online:) Rate predictions showing the reduction of rate uncertainty by this work, assuming Q = 639 (82) keV. We only consider uncertainties from resonance energy errors. The light band (blue) shows the 1- uncertainty in the shell model rate, whereas the dark band (grey) shows the 1- uncertainty in the experimentally-constrained rate. A clear reduction of the rate uncertainty in the temperature region of interest can be seen, especially at lower temperatures.
T (cm/s/mole)
Recommended Lower Upper
0.1 1.497e-19 8.583e-20 2.422e-19
0.2 8.661e-12 8.121e-12 1.082e-11
0.3 1.666e-08 1.183e-08 2.084e-08
0.4 1.244e-06 7.796e-07 1.746e-06
0.5 1.859e-05 1.237e-05 3.606e-05
0.6 1.156e-04 8.254e-05 2.911e-04
0.7 4.677e-04 3.197e-04 1.357e-03
0.8 1.529e-03 8.877e-04 4.423e-03
0.9 3.880e-03 2.009e-03 1.149e-02
1.0 8.951e-03 4.287e-03 2.551e-02
1.5 1.583e-01 8.221e-02 3.294e-01
2.0 9.620e-01 6.177e-01 1.655e+00
Table 4: The recommended reaction rate as a function of temperature (GK) from this work, together with 1- uncertainties (higher and lower).
1224 1.052854 -6.805068 7.127737E-01 -1.049583 5.849955E-02 -3.234916E-03 -9.787774E-01
Other -5.223069E+01 -9.902812 1.336866E+02 -7.623392E+01 -8.335959E-01 2.019964E-01 6.914259E+01
1038 -5.177171 -4.627019 -7.755680E-02 8.817104E-02 -4.086783E-03 1.981643E-04 -1.549327
826 -2.601956E+01 -2.170262 4.521332E-04 -6.347735E-04 3.674535E-05 -2.248394E-06 -1.499681
Table 5: REACLIB fit coefficients for our recommended Ni(p,) reaction rate.

V Consequences on the rp-process flow around Ni

The astrophysical conditions that would lead the rp-process flow to bypass the Ni waiting point were investigated using a limited reaction network that includes the nuclides in Fig. 1. The network was seeded with Ni, where the rp-process enters the A = 56 region. Ni was treated as a sink in the network calculation, with only flow into this nuclide being allowed. In this case, the ratio of the abundance of all other nuclei (Ni, Cu, and Zn) to the total abundance in the and chains is a measure of the fraction of the rp-process reaction flow that bypasses Ni, as it measures the amount of material trapped in neither Co nor Ni. The reaction network was run at constant temperature and proton density for 1 s, approximately 5 half-lives of Ni. A constant proton density was ensured by keeping the mass density constant, and by using a large proton-to-seed ratio of 400 such that the change in the proton abundance due to the comsumption of protons is negligible.

Figure 7: (Color online:) Phase space diagram showing the region where the bypass may be effective, demonstrating the impact of the remaining nuclear physics uncertainties. The color and contours indicate the strength of the bypass. The most unfavorable (left) and most favorable (right) conditions are chosen to demonstrate the full range of the uncertainties.

Even with the constraint on the Ni(p,) rate from this work, there remain additional uncertainties that affect the rp-process flow. The proton-capture rate on Cu determines the branching at Cu, where decay leads back to Ni, and also determines the total proton-capture flow at Ni in the case of equilibrium between Ni and Cu. In addition, the mass of Zn has not been measured and its uncertainty affects the Zn(,p) rate, which hampers the flow bypassing Ni at high temperatures. Finally, the uncertain 78 17 -delayed proton branch of Zn Blank et al. (2007) directs the reaction flow back to Ni and needs to be better constrained. To explore the effect of these uncertainties, we considered two scenarios of maximal and minimal favorability for the bypass. In the case of the maximal (minimal) favorability: (1) the Cu(p,) rate was increased (decreased) by a factor of 100, the expected uncertainty of a shell-model rate; (2) the Ni(p,) rate was increased (decreased) by the uncertainty reported in this work; (3) the -delayed proton-emission rate of Zn was decreased (increased) by the uncertainty reported by Blank et al. (2007).
Fig. 7 shows the resulting fraction of the reaction flow that bypasses Ni as a function of temperature and proton density for the two scenarios. In the scenario with the most favorable nuclear physics assumptions, Ni is significantly bypassed for temperatures in the range of about 0.4 - 1.2 GK and proton densities above 10 g/cm. These are within the range of typical X-ray burst conditions, with peak temperatures of 1-2 GK and proton densities up to 10 g/cm. On the other hand, for the most unfavorable scenario proton densities in excess of 10 g/cm are required for the reaction flow to bypass Ni. Therefore, in the favorable scenario, Ni would be partially bypassed by the rp-process in all X-ray bursts, while in the unfavorable scenario the full rp-process would always pass through Ni.

Vi Conclusion

This work presents the first experimentally-constrained Ni(p,)Cu thermonuclear reaction rate, utilizing 5 newly identified excited states in Cu, a new theoretically-constrained reaction Q-value, and a new shell-model calculation of - and proton-widths. Below a temperature of 0.5 GK, the experimental data reduce the rate uncertainty from a factor of 10 to 10 at 0.1 GK and by almost an order of magnitude at 0.5 GK . The dominant remaining uncertainty is the reaction Q-value due to the unknown mass of Cu. For temperatures above 0.5 GK, the reaction rate is dominated by higher-lying resonances that have not been determined experimentally. With the new data, and using a detailed network analysis, we find that within remaining uncertainties the rp-process can bypass the Ni waiting point for typical x-ray burst conditions with a bypass branch as high as 40. We also identify additional nuclear physics uncertainties in the Cu(p,) reaction rate, the Zn mass, and the Zn -delayed proton emission branch that need to be addressed.

The authors want to thank the staff and the beam operators at the NSCL for their effort during the experiment. This work is supported by NSF Grants No. PHY11-02511, No. PHY10-68217, No. PHY14-04442, No. PHY08-22648 (Joint Institute for Nuclear Astrophysics), and No. PHY14-30152 (JINA Center for the Evolution of the Elements). GRETINA was funded by the U.S. DOE Office of Science. Operation of the array at NSCL is supported by NSF under Cooperative Agreement PHY11-02511 (NSCL) and DOE under Grant No. DE-AC02-05CH11231 (LBNL).

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