High-precision mass measurement of {}^{56}Cu and the redirection of the rp-process flow

High-precision mass measurement of $^{56}$Cu and the redirection of the rp-process flow

Abstract

We report the mass measurement of Cu, using the LEBIT 9.4T Penning trap mass spectrometer at the National Superconducting Cyclotron Laboratory at Michigan State University. The mass of Cu is critical for constraining the reaction rates of the Ni(p,)Cu(p,)Zn()Cu bypass around the Ni waiting point. Previous recommended mass excess values have disagreed by several hundred keV. Our new value, ME= keV, is a factor of 30 more precise than the suggested value from the 2012 atomic mass evaluation [Chin. Phys. C 36, 1603 (2012)], and more than a factor of 12 more precise than values calculated using local mass extrapolations, while agreeing with the newest 2016 atomic mass evaluation value [Chin. Phys. C 41, 030003 (2017)]. The new experimental average was used to calculate the astrophysical Ni(p,) and Zn(,p) reaction rates and perform reaction network calculations of the rp-process. These show that the rp-process flow redirects around the Ni waiting point through the Ni(p,) route, allowing it to proceed to higher masses more quickly and resulting in a reduction in ashes around this waiting point and an enhancement to higher-mass ashes.

pacs:

Type I X-ray bursts are astronomical events that occur in binary systems where a neutron star accretes hydrogen and helium-rich material from its companion star; the accretion of more matter on the surface of the neutron star results in increasing densities and temperatures until the accreted material undergoes a thermonuclear runaway Woosley and Taam (1976). The energy generated during this thermonuclear runaway gives rise to an increase in temperature and sharp increase of X-ray luminosity followed by a slower decay as the atmosphere cools.

The high temperatures and densities achieved during this event provide the conditions necessary to trigger the rapid proton capture (rp) process, a production mechanism for proton-rich nuclei beyond the iron peak and lighter than Wallace and Woosley (1981); Schatz et al. (2001). The rp-process flows through a series of proton capture (p,), photodisintegration (,p), capture (,p) and -decay reactions, with relative rates of reactions determining the pathway. Type I X-ray bursts generally have rise times of -10 s, and decay times ranging from 10 s to several minutes, though much longer-lived superbursts, with hour-long decay times, also exist Parikh et al. (2013).Bottlenecks in the rp-process reaction pathway are created where the low proton-capture values make photodisintegration competitive with proton-capture and decays become the dominant route. Where the decay half-life is long, relative to the timescale of the X-ray burst, a waiting point occurs. The interplay of various other factors also affects the reaction flow and thus the significance of these waiting points. Of particular importance is the relative intensity of the (p,) and (,p) reaction rates, which is highly sensitive to the values of the reactions Parikh et al. (2009).

With a small value for the reaction of keV Wang et al. (2017) and an hours-long stellar half-life Fuller et al. (1982), the doubly-magic nucleus Ni is one of the most important rp-process waiting points Kankainen et al. (2010). Indeed, it was historically thought to be the endpoint of the rp-process Wallace and Woosley (1981), though we now know it proceeds to higher masses Schatz et al. (2001); Elomaa et al. (2009). The flow through Ni is well-characterized, based on values Kankainen et al. (2010); Wang et al. (2017), as well as Ni(p,) Rehm et al. (1998) and Cu(p,) Langer et al. (2014) reaction rates. A route starting at Ni could allow rp-process flow to bypass the Ni waiting point through Ni(p,)Cu(p,)Zn()Cu but it is not as well characterized; the branching of the flow at Ni between the two routes is determined by the decay rate and the Ni(p,) and Cu(,p) reaction rates.

The astrophysical rates of these (p,) reactions can be approximated by Iliadis (2007):

(1)

where is the th resonance for excitation energy , is the value of the reaction, the difference in mass between the initial and final states, and is the th resonance strength, determined by:

(2)

where , and are the spins of the resonance, proton, and ground-state proton-capturing nucleus, respectively, and and are the and proton partial widths. Recently, the low-lying level scheme of Cu was experimentally determined for the first time Ong et al. (2017), leaving the largest source of uncertainty in the critical Ni(p,) rate to be the proton separation energy of Cu.

Because of its high astrophysical importance, several predictions of the Cu atomic mass have been made recently using the Coulomb Displacement Energy (CDE) mass relation Tu et al. (2016), and the Isobaric Mass Multiplet Equation (IMME) Ong et al. (2017). Furthermore, the Atomic Mass Evaluation (Ame) predictions varied by several hundreds of keV from Ame2003 Audi et al. (2003) to Ame2012 Wang et al. (2012). Moreover, for reaction network calculations, the masses of rp-process nuclei must be measured accurately to within 10 keVSchatz (2006), a precision which is not achieved by any of the current predictions. The recently released Ame2016 includes an unpublished atomic mass from a private communication with P. Zhang et al.Wang et al. (2017) which also fails to achieve the necessary precision. Hence, we performed a high-precision mass measurement of Cu using Penning trap mass spectrometry, the most accurate available technique, to confirm the accuracy of that value while attaining the precision necessary for reaction network calculations to determine the flow of the rp-process around Ni.

In this Letter, we report the first Penning trap mass measurement of Cu, produced at the National Superconducting Cyclotron Laboratory (NSCL) and measured at the Low-Energy Beam and Ion Trap (LEBIT) facility Ringle et al. (2013). The LEBIT facility is unique among Penning trap mass spectrometry facilities in its ability to perform high-precision mass measurements on rare isotopes produced by projectile fragmentation. In this experiment, radioactive Cu was produced by impinging a 160 MeV/u primary beam of Ni on a 752 mg/cm beryllium target at the Coupled Cyclotron Facility at the NSCL. The resulting beam passed through the A1900 fragment separator with a 294 mg/cm aluminum wedge Morrissey et al. (2003) to separate the secondary beam. This beam consisted of Cu (2.6%), with contaminants of Ni, Co, and Mn.

The beam then entered the beam stopping area Cooper et al. (2014) through a momentum compression beamline, where it was degraded with aluminum degraders of 205 m and 523 m thickness before passing through a 1010 m, 3.1 mrad aluminum wedge and entering the gas cell with an energy of less than 1 MeV/u. In the gas cell, ions were stopped through their collision with the high-purity helium gas at a pressure of about 73 mbar; during this process, the highly-charged ions recombined down to a singly charged state. These ions were transported by a combination of RF and DC fields as well as gas flow through the gas cell, and were then extracted into a radiofrequency quadrupole (RFQ) ion-guide and transported through a magnetic dipole mass separator with a resolving power greater than . Transmitted activity after the mass filter was measured using an insertable Si detector. The most activity was found with , corresponding to the extraction of as an adduct with two waters, . Following the mass separator, the ions then entered the LEBIT facility.

In the LEBIT facility, the ions were first injected into the cooler-buncher, a two-staged helium-gas-filled RFQ ion trap Schwarz et al. (2016). In the first stage, moderate pressure helium gas was used to cool the ions in a large diameter RFQ ion guide. The potential difference of 55 V from the gas cell accelerated the ions into the helium gas to strip the water ligands, following the molecular-breaking technique previously used at LEBIT Schury et al. (2006). The ions were accumulated, cooled, and released to the LEBIT Penning trap in pulses of approximately 100 ns Ringle et al. (2009). To further purify the beam, a fast kicker in the beam line between the cooler-buncher and the Penning trap was used as a time-of-flight mass separator to select ions of , corresponding to and unwanted molecular contaminants of the same .

The 9.4T Penning trap at the LEBIT facility consists of a high-precision hyperbolic electrode system contained in an actively-shielded magnet system Ringle et al. (2013). Electrodes in front of the Penning trap are used to decelerate the ion pulses to low energy before entering the trap. The final section of these electrodes are quadrisected radially to form a “Lorentz steerer” Ringle et al. (2007a) that forces the ion to enter the trap off-axis and perform a magnetron motion of frequency once the trapping potential is on.

Figure 1: (color online). A sample 50-ms time-of-flight ion cyclotron resonance used for the determination of the frequency ratio of . The solid red curve represents a fit of the theoretical profile König et al. (1995).

After their capture, the ions were purified, using both dipole cleaning Blaum et al. (2004) and the stored waveform inverse Fourier transform (SWIFT) technique Kwiatkowski et al. (2015). Both techniques excite contaminant ions using azimuthal RF dipole fields at their reduced cyclotron frequency, , driving them to a large enough radius such that they do not interfere with the measurement. In the dipole technique, specific contaminants are identified for cleaning Blaum et al. (2004). In the SWIFT technique, an RF dipole drive is applied to a range of frequencies surrounding but excluding the reduced cyclotron frequency of the ion of interest, cleaning nearby contaminants without the need to specifically identify them Kwiatkowski et al. (2015); Guan and Marshall (1996). Then, the time-of-flight ion cyclotron resonance technique (TOF-ICR) Bollen et al. (1990); König et al. (1995) was used to determine the ions’ cyclotron frequency.

In these measurements, either a 50-ms, 75-ms, or 100-ms quadrupole excitation was used. These resonances were then fitted to the theoretical line shape König et al. (1995), and the cyclotron frequency was thus determined; a sample 50-ms resonance of can be seen in Fig. 1. Between measurements of the cyclotron frequency, measurements of the reference molecular ion cyclotron frequency were conducted. The molecule is possibly the result of an = 92 hydrocarbon molecule extracted from the gas cell and coming with the molecule broken by collision-induced dissociation Schury et al. (2006).

In Penning trap mass spectrometry, the experimental result is the frequency ratio , where is the interpolated cyclotron frequency from the measurements bracketing the measurements. Then, using the average of multiple frequency ratios the atomic mass is given by:

(3)

where is the atomic mass of the neutral reference atom or molecule, and the electron mass. The electron ionization energies and the molecular binding energy of , both on the order of eVs, were not included as they are several orders of magnitude smaller than the statistical uncertainty of the measurement.

Figure 2: Measured cyclotron frequency ratios relative to the average value ; the grey bar represents the uncertainty in .

A series of 17 measurements of the cyclotron frequency were taken over a 40-hour period and the weighted average of these measurements is 1.01641577(12). As seen in Fig. 2, the individual values of scatter statistically about the average .

Most systematic uncertainties in the measured frequency ratios scale linearly with the mass difference between the ion of interest and the calibrant ion. These systematic effects include: magnetic field inhomogeneities, trap misalignment with the magnetic field, harmonic distortion of the electric potential and non-harmonic imperfections in the trapping potential Bollen et al. (1990). These mass dependent shifts to , have been studied at LEBIT and found to be at the level of /u Gulyuz et al. (2015), negligible compared to the statistical uncertainty on .

Remaining systematic effects include non-linear time-dependent changes in the magnetic field, relativistic effects on the cyclotron frequency, and ion-ion interaction in the trap. Previous work has shown that the effect of nonlinear magnetic field fluctuations on the ratio should be less than over an hour Ringle et al. (2007b), which was our measurement time. Relativistic effects on the cyclotron frequency were found to be negligible due the large mass of the ions involved. Finally, isobaric contaminants present in the trap during a measurement could lead to a systematic frequency shift Bollen et al. (1992); this effect was minimized by removing most of the contamination using the SWIFT and dipole excitations and by limiting the total number of ions in the trap. For Cu, the incident rate limited it to two or fewer detected ions in the trap. The was limited to five or fewer detected ions in the trap; a z-class analysis was performed, and any count-dependent shifts to were found to be more than an order of magnitude smaller than the statistical uncertainty.

Other possible systematics unaccounted for were probed through a measurement of the ratio of stable potassium isotopes; , with SWIFT being used on the K measurement but not for the K reference, as in the experiment. Potassium was produced using the LEBIT offline thermal ion source and otherwise treated in the same way as the ions produced online. The measured value agrees with the accepted ratio to within a Birge ratio Birge (1932) scaled uncertainty smaller than ; individual values can be seen in Fig. 3. Thus, any mass dependent shifts either from the usage of SWIFT or the difference in mass are negligible compared to the statistical uncertainty on the measurement. Finally, the Birge ratio for the measurement was 1.11(12), which indicates that the fluctuations in Fig. 2 are statistical in nature.

Figure 3: Difference of measured values of relative to the value calculated from Ame2016 Wang et al. (2017). The grey bar represents the average value and its uncertainty; the uncertainty of the Ame2016 value, , is not visible on this graph.

The resulting mass excess is reported in Table 1 as well as the recommended value from the two previous Atomic Mass Evaluations Audi et al. (2003); Wang et al. (2012), Coulomb Displacement Energy Tu et al. (2016), and the Isobaric Mass Multiplet Equation Ong et al. (2017) predictions and the latest result from Ame2016 Wang et al. (2017). Our new Cu mass results in a proton separation energy of keV, calculated from using our new Cu mass and the masses of Ni and H from Ame2016 Wang et al. (2017).

Ref. ME (keV) (keV)
This work -38 626.7(6.4) 579.8(6.4)
Ame2016 Wang et al. (2017) -38 643(15) 596(15)
Experimental Average -38 629.2(5.9) 582.3(5.9)
Ong et al. Ong et al. (2017) -38 685(82) 639(82)
Tu et al. Tu et al. (2016) -38 697(88) 651(88)
Ame2003 Audi et al. (2003) -38 600(140) 560(140)
Ame2012 Wang et al. (2012) -38 240(200) 190(200)
Table 1: A comparison of mass excesses and proton separation energies for Cu from CDE calculations Tu et al. (2016), IMME calculation Ong et al. (2017), and the recommended values from the last three atomic mass evaluations, and the weighted average of the two experimental measurements.

Using the weighted average of our new Cu mass and the Ame16 value, also available in Table 1, and the level scheme established in Ong et al. (2017), a new astrophysical reaction rate for was calculated. The proton and widths, and , were calculated for each state using a shell model with the GXPF1A interaction Honma et al. (2005). Up to three-particle-three-hole excitations in the shell were allowed in this calculation Ong et al. (2017), with the proton and widths and resonance strengths scaled appropriately. A Monte Carlo approach, similar to that in Iliadis et al. (2015); Ong et al. (2017), was used to calculate uncertainties. At a given temperature, the 50th percentile of the distribution of calculated rates gives the median rate, and the 16th and 84th percentiles the 1 uncertainties. The results can be seen in Fig. 4, compared with the results found using the extrema of the calculated Cu masses, Ame2012Wang et al. (2012) and Tu et al. Tu et al. (2016); this shows that the (p,) reaction dominates up to GK, slightly lower than the Tu et al. case, and significantly higher than the Ame2012 case, where the reverse rate always dominates. For the Ame2012 mass, at low temperatures, direct capture dominates, leading to little uncertainty, but at higher temperatures, the reaction can access resonant states and the mass uncertainty dominates. The uncertainty of the rate at low temperatures for the Tu et al. value is dominated by the potential of the 573 keV state to act as a resonance within the 1- lower bound of the value; this is also why the median rate is near the lower bound. Our mass shows a reduced uncertainty when compared to both prior masses, as the value uncertainty is now comparable to the uncertainty in resonance energies.

Figure 4: (color online) Rate for the reaction and 1 uncertainties for Ame2012 (black band) and Tu et al. calculated values (red band) and using our new mass measurement (blue band). The prior reverse rates (dashed lines) and new recommended reverse rate (dashed blue line) from this work are also shown.
Figure 5: (color online) Fractional difference of abundance by mass number of this work (solid black) compared to that using the masses suggested, in Ame2012Wang et al. (2012) and the same fractional difference using Tu et al.Tu et al. (2016) (dashed red).

A single-zone X-ray burst model was then run using the new Cu mass with an ignition temperature of 0.386 GK, ignition pressure of 1.73 10 erg cm and initial hydrogen and helium mass fractions of 0.51 and 0.39 respectively, demonstrated by Cyburt et al. (2016) to produce light curves and ash compositions to most closely match those of multi-zone models, and with a peak temperature of 1.17 GK. As can be seen in Fig. 5, the final abundances produced by this calculation demonstrate the extent to which the bypass due to the change in (p,)-(,p) equilibrium is active, showing a reduction in abundance in the mass range around the Ni waiting point in comparison to ones based on the suggested Ame2012 value, though not as extreme as the one seen with the mass from Tu et al.; the maximal bypass is 39%, with a typical X-ray burst trajectory having a bypass of 15%. The percentage increase in heavier mass ashes is not as apparent due to the higher absolute abundance of heavier ashes at around mass 60. This means the newly-calculated reaction rate allows the rp-process flow to bypass the waiting point and proceed more quickly through the region.

In summary, the high precision measurement of the mass of Cu is reported, allowing the calculation of its proton separation energy to a precision of 6.5 keV, a factor of 30 improvement over the Ame2012 suggested value and a factor of more than 12 improvement over the IMME and CDE calculated values Ong et al. (2017); Tu et al. (2016) while agreeing with the private communication available in Ame2016 Wang et al. (2017). New thermonuclear reaction rates were then calculated using the first experimental mass of Cu, the weighted average of our new value and the Ame2016 value, and abundances for the rp-process around the Ni waiting point were determined. These abundances show that the new reaction rate allows the rp-process to redirect around this waiting point and proceed to heavier masses more quickly, resulting in an enhancement in higher-mass ashes. The dominant sources of uncertainty are now the unmeasured widths and for the Ni(p,) reaction; the unmeasured higher-lying level scheme of Cu; the unmeasured Zn mass for the Cu(p,) and Zn(,p) reactions, which hampers this flow from bypassing Ni at high temperatures; and the high uncertainty on the -delayed proton branch of Zn (78(17)%, Blank et al. (2007)), which directs flow back to Ni.

The authors would like to acknowledge Hendrik Schatz for fruitful discussions related to the work presented in this Letter. This work was conducted with the support of Michigan State University, the National Science Foundation under Contract No. PHY-1102511 and No. PHY-1713857, and the US Department of Energy, Office of Science, Office of Nuclear Physics under award number DE-SC0015927. The work leading to this publication has also been supported by a DAAD P.R.I.M.E. fellowship with funding from the German Federal Ministry of Education and Research and the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007/2013) under REA Grant Agreement No. 605728.

References

  1. S. E. Woosley and R. E. Taam, Nature 263, 101 (1976).
  2. R. K. Wallace and S. E. Woosley, Astrophys. J. Suppl. Ser. 45, 389 (1981).
  3. H. Schatz, A. Aprahamian, V. Barnard, L. Bildsten, A. Cumming, M. Ouellette, T. Rauscher, F.-K. Thielemann,  and M. Wiescher, Phys. Rev. Lett. 86, 3471 (2001).
  4. A. Parikh, J. José, G. Sala,  and C. Iliadis, Progress in Particle and Nuclear Physics 69, 225 (2013).
  5. A. Parikh, J. José, C. Iliadis, F. Moreno,  and T. Rauscher, Phys. Rev. C 79, 045802 (2009).
  6. M. Wang, G. Audi, F. Kondev, W. Huang, S. Naimi,  and X. Xu, Chinese Physics C 41, 030003 (2017).
  7. G. M. Fuller, W. A. Fowler,  and M. J. Newman, The Astrophysical Journal 252, 715 (1982).
  8. A. Kankainen, V.-V. Elomaa, T. Eronen, D. Gorelov, J. Hakala, A. Jokinen, T. Kessler, V. S. Kolhinen, I. D. Moore, S. Rahaman, M. Reponen, J. Rissanen, A. Saastamoinen, C. Weber,  and J. Äystö, Phys. Rev. C 82, 034311 (2010).
  9. V.-V. Elomaa, G. K. Vorobjev, A. Kankainen, L. Batist, S. Eliseev, T. Eronen, J. Hakala, A. Jokinen, I. D. Moore, Y. N. Novikov, H. Penttilä, A. Popov, S. Rahaman, J. Rissanen, A. Saastamoinen, H. Schatz, D. M. Seliverstov, C. Weber,  and J. Äystö, Phys. Rev. Lett. 102, 252501 (2009).
  10. K. E. Rehm, F. Borasi, C. L. Jiang, D. Ackermann, I. Ahmad, B. A. Brown, F. Brumwell, C. N. Davids, P. Decrock, S. M. Fischer, J. Görres, J. Greene, G. Hackmann, B. Harss, D. Henderson, W. Henning, R. V. F. Janssens, G. McMichael, V. Nanal, D. Nisius, J. Nolen, R. C. Pardo, M. Paul, P. Reiter, J. P. Schiffer, D. Seweryniak, R. E. Segel, M. Wiescher,  and A. H. Wuosmaa, Phys. Rev. Lett. 80, 676 (1998).
  11. C. Langer, F. Montes, A. Aprahamian, D. W. Bardayan, D. Bazin, B. A. Brown, J. Browne, H. Crawford, R. H. Cyburt, C. Domingo-Pardo, A. Gade, S. George, P. Hosmer, L. Keek, A. Kontos, I.-Y. Lee, A. Lemasson, E. Lunderberg, Y. Maeda, M. Matos, Z. Meisel, S. Noji, F. M. Nunes, A. Nystrom, G. Perdikakis, J. Pereira, S. J. Quinn, F. Recchia, H. Schatz, M. Scott, K. Siegl, A. Simon, M. Smith, A. Spyrou, J. Stevens, S. R. Stroberg, D. Weisshaar, J. Wheeler, K. Wimmer,  and R. G. T. Zegers, Phys. Rev. Lett. 113, 032502 (2014).
  12. C. Iliadis, Nuclear physics of stars (John Wiley & Sons, 2007).
  13. W.-J. Ong, C. Langer, F. Montes, A. Aprahamian, D. W. Bardayan, D. Bazin, B. A. Brown, J. Browne, H. Crawford, R. Cyburt, E. B. Deleeuw, C. Domingo-Pardo, A. Gade, S. George, P. Hosmer, L. Keek, A. Kontos, I.-Y. Lee, A. Lemasson, E. Lunderberg, Y. Maeda, M. Matos, Z. Meisel, S. Noji, F. M. Nunes, A. Nystrom, G. Perdikakis, J. Pereira, S. J. Quinn, F. Recchia, H. Schatz, M. Scott, K. Siegl, A. Simon, M. Smith, A. Spyrou, J. Stevens, S. R. Stroberg, D. Weisshaar, J. Wheeler, K. Wimmer,  and R. G. T. Zegers, Phys. Rev. C 95, 055806 (2017).
  14. X. Tu, Y. Litvinov, K. Blaum, B. Mei, B. Sun, Y. Sun, M. Wang, H. Xu,  and Y. Zhang, Nuclear Physics A 945, 89 (2016).
  15. G. Audi, A. Wapstra,  and C. Thibault, Nuclear Physics A 729, 337 (2003), the 2003 NUBASE and Atomic Mass Evaluations.
  16. M. Wang, G. Audi, A. H. Wapstra, F. G. Kondev, M. MacCormick, X. Xu,  and B. Pfeiffer, Chin. Phys. C 36, 1603 (2012).
  17. H. Schatz, International Journal of Mass Spectrometry 251, 293 (2006).
  18. R. Ringle, G. Bollen,  and S. Schwarz, Int. J. Mass Spectrom. 349–350, 87 (2013).
  19. D. J. Morrissey, B. M. Sherrill, M. Steiner, A. Stolz,  and I. Wiedenhoever, Nucl. Instrum. Methods Phys. Res., Sect. B 204, 90 (2003).
  20. K. Cooper, C. S. Sumithrarachchi, D. J. Morrissey, A. Levand, J. A. Rodriguez, G. Savard, S. Schwarz,  and B. Zabransky, Nucl. Instrum. Methods Phys. Res., Sect. A 763, 543 (2014).
  21. S. Schwarz, G. Bollen, R. Ringle, J. Savory,  and P. Schury, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 816, 131 (2016).
  22. P. Schury, G. Bollen, M. Block, D. J. Morrissey, R. Ringle, A. Prinke, J. Savory, S. Schwarz,  and T. Sun, Hyperfine Interactions 173, 165 (2006).
  23. R. Ringle, G. Bollen, A. Prinke, J. Savory, P. Schury, S. Schwarz,  and T. Sun, Nucl. Instrum. Methods Phys. Res., Sect. A 604, 536 (2009).
  24. R. Ringle, G. Bollen, A. Prinke, J. Savory, P. Schury, S. Schwarz,  and T. Sun, Int. J. Mass Spectrom. 263, 38 (2007a).
  25. M. König, G. Bollen, H.-J. Kluge, T. Otto,  and J. Szerypo, Int. J. Mass Spectrom. 142, 95 (1995).
  26. K. Blaum, D. Beck, G. Bollen, P. Delahaye, C. Guénaut, F. Herfurth, A. Kellerbauer, H.-J. Kluge, D. Lunney, S. Schwarz, L. Schweikhard,  and C. Yazidjian, EPL (Europhysics Letters) 67, 586 (2004).
  27. A. Kwiatkowski, G. Bollen, M. Redshaw, R. Ringle,  and S. Schwarz, International Journal of Mass Spectrometry 379, 9 (2015).
  28. S. Guan and A. G. Marshall, International Journal of Mass Spectrometry and Ion Processes 157, 5 (1996).
  29. G. Bollen, R. B. Moore, G. Savard,  and H. Stolzenberg, J. Appl. Phys. 68, 4355 (1990).
  30. K. Gulyuz, J. Ariche, G. Bollen, S. Bustabad, M. Eibach, C. Izzo, S. J. Novario, M. Redshaw, R. Ringle, R. Sandler, S. Schwarz,  and A. A. Valverde, Phys. Rev. C 91, 055501 (2015).
  31. R. Ringle, T. Sun, G. Bollen, D. Davies, M. Facina, J. Huikari, E. Kwan, D. J. Morrissey, A. Prinke, J. Savory, P. Schury, S. Schwarz,  and C. S. Sumithrarachchi, Phys. Rev. C 75, 055503 (2007b).
  32. G. Bollen, H.-J. Kluge, M. König, T. Otto, G. Savard, H. Stolzenberg, R. B. Moore, G. Rouleau, G. Audi,  and I. Collaboration, Phys. Rev. C.. 46, R2140 (1992).
  33. R. T. Birge, Phys. Rev. 40, 207 (1932).
  34. M. Honma, T. Otsuka, B. A. Brown,  and T. Mizusaki, The European Physical Journal A - Hadrons and Nuclei 25 (2005), 10.1140/epjad/i2005-06-032-2.
  35. C. Iliadis, R. Longland, A. Coc, F. X. Timmes,  and A. E. Champagne, Journal of Physics G: Nuclear and Particle Physics 42, 034007 (2015).
  36. R. H. Cyburt, A. M. Amthor, A. Heger, E. Johnson, L. Keek, Z. Meisel, H. Schatz,  and K. Smith, The Astrophysical Journal 830, 55 (2016).
  37. B. Blank, C. Borcea, G. Canchel, C. E. Demonchy, F. de Oliveira Santos, C. Dossat, J. Giovinazzo, S. Grévy, L. Hay, P. Hellmuth, S. Leblanc, I. Matea, J. L. Pedroza, L. Perrot, J. Pibernat, A. Rebii, L. Serani,  and J. C. Thomas, The European Physical Journal A 31, 267 (2007).
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
239025
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description