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Weak interaction strengths for supernovae calculations via the (t,3He) reaction on medium-heavy nuclei
Nuclear Physics A 758 (2005) 67c–70c
Weak interaction strengths for supernovae calculations via the (t,3 He) reaction on medium-heavy nuclei. R.G.T. Zegersa∗ A. L. Colea , H. Akimuneb , S.M. Austina , D. Bazina , A.M. van den Bergc , G.P.A. Bergc , J. Brownd , I. Daitoe , Y. Fujitaf , M. Fujiwarag , K. Harag , M.N. Harakehc , G.W. Hitta , M.E. Howardh , J. J¨aneckei , T. Kawabataj, T. Nakamurak , H. Uenol , H. Schatza , B.M. Sherrilla , M. Steinera a National Superconducting Cyclotron Laboratory, the Joint Institute for Nuclear Astrophysics and the Department of Physics, Michigan State University, MI 48824-1321, USA b c
Department of Physics, Konan University, Kobe, Hyogo 658-8501, Japan
Kernfysisch Versneller Insituut, Zernikelaan 25, 9747 AA Groningen, The Netherlands
d
Department of Physics, Wabash College, Crawfordsville, IN 47933, USA
e
Advanced Photon Research Center, Japan Atomic Research Institute, Kizu, Kyoto 619-0215, Japan
f
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
g
Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan
h
Physics Department, Ohio State University, Columbus, OH 43210, USA
i
Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
j
Center for Nuclear Study, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
k
Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 O-Okayama, Tokyo 152-8550, Japan l
Applied Nuclear Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan
The 58 Ni(t,3 He)58 Co reaction at 112 MeV/nucleon was measured to identify strength associated with Gamow-Teller transitions in the Tz = +1 direction. The experiment is a test case for future similar studies. The main aim of such studies is to test theoretical models used to predict Gamow-Teller strength distributions that serve as input for su∗
This work was supported by the US NSF (PHY02-16783, Joint Institute for Nuclear Astrophysics and PHY 0110253), The Ministry of Education, Science, Sports and Culture of Japan, the Stichting voor Fundamenteel Onderzoek der Materie (FOM), the Netherlands and by the Office of the Vice President for Research, University of Michigan.
0375-9474/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2005.05.018
68c
R.G.T. Zegers et al. / Nuclear Physics A 758 (2005) 67c–70c
pernovae evolution calculations. The results indicate that the (t,3 He) reaction is indeed a powerful tool to perform such tests. 1. Motivation In the later stages of stellar evolution, processes governed by the weak interaction determine the core entropy and electron to baryon ratio of the pre-supernova star. Electron capture (EC) reduces the number of electrons and beta decay works in the opposite direction. While Fermi transitions that play a role in beta decay are trivial to calculate, Gamow-Teller (GT) transitions (for both EC and beta decay) are difficult to predict. Initially, weak interaction rates by Fuller, Fowler and Newman (FFN) [1] based on an independent-particle model (IPM) were used for calculations with astrophysical purposes. However, the GT strength is strongly quenched and fragmented compared to IPM estimates due to residual interactions amongst the valence nucleons [2]. Hence, stellar weak interaction rates have been recalculated taking into account such effects for sd-shell nuclei [3] and pf-shell nuclei [4,5]. It was shown that these new estimates strongly affect the late evolution of stars [6] and that especially odd-N nuclei play an important role. When the collapse of the star occurs, a large fraction of the matter survives in heavy nuclei [7]. In describing the evolutionary path, EC is currently treated schematically: an IPM model is used in which GT transitions are Pauli blocked for nuclei with N>40 and Z<40 and do not provide EC strength. Again, due to residual interaction, this picture is too simple. Pauli unblocking can occur due to residual interactions. Moreover, because of the finite temperature in stars, further unblocking is possible. Shell-model calculations used for lighter nuclei are not yet feasible for these heavier nuclei and shell-model MonteCarlo calculations are used instead [8]. Such studies indicate that GT transitions are not fully Pauli blocked and dominate the EC process at stellar conditions since the number of available free protons is small compared to the number of heavier nuclei [9]. Because of these astrophysical applications, a push to measure GT transitions in mediumheavy nuclei (Fe-region) has been made. Different (n,p)-type reactions (∆Tz = +1) are used as a probe and all rely on the linear correlation between GT-strength [B(GT)] and the GT cross section at zero momentum transfer(q=0): dσ (q = 0) = KND | Jστ |2 B(GT ), (1) dΩ where K is a kinematical factor, ND the distortion factor and | Jστ |2 the volume integral of the nucleon-nucleus interaction. For the fundamental (p,n) charge-exchange reactions (and thus (n,p) as well), equation 1 has been tested in detail [10] and, except for a few cases, was found to be valid. Therefore, the (n,p) reaction seems to be the best probe to measure GT strength in the ∆Tz = +1 direction. Indeed, a fair amount of measurements have been performed [11]. However, due to the limited resolution (∼ 1 MeV) and the difficulty in producing intense neutron beams, the focus has shifted to other probes. The (d,2 He) reaction has been employed with good success (see e.g. [12,13]), due to the high resolutions obtained and the selectivity for spin-flip transitions. However, the reaction mechanism is complex since the ejectile is unbound. Also, the energy is somewhat low (85 MeV/nucleon) to ensure that linearity between cross section at q = 0 and B(GT) is maintained.
69c
R.G.T. Zegers et al. / Nuclear Physics A 758 (2005) 67c–70c
2
a)
dσ/dΩ (mb/sr)
1 0 3
3
58
Ni(t, He) Co Et=112 MeV/nucleon c) 0o-3o Result from MDA scaled to B(GT) 0.75 2 RY from (d, He) B(GT)
58
A
IN
b)
0oo-1oo 2 -3
GT
E PR
LIM 0.5
0.25
2 1 0
0
2.5
5
7.5 58
10
Ex( Co) (MeV)
0
0
2.5
5
7.5
10 58
Ex( Co)
Figure 1. Preliminary results for the 58 Ni(t,3 He)58 Co reaction at 112 MeV/nucleon: (a) differential cross section for θcm (t) < 3o . (b) same as (a), but for θcm (t) < 1o (full) and 2o < θcm (t) < 3o (dashed). Main components of the GT strength are indicated. (c) GTstrength extracted through MDA. The main GT-peak is at present scaled to the value obtained from the 58 Ni(d,2 He) reaction [13].
The (t,3 He) reaction at energies above 100 MeV/nucleon is an attractive alternative. The reaction mechanism is simple and can be tested in detail using the inverse reaction for which many data are available. The high energy ensures a strong preference for spinflip transitions and only minor contributions due to multi-step processes and the tensor-τ dσ component of the nucleon-nucleus interaction which break the B(GT)- dΩ (q = 0) linearity. Therefore, this probe has been developed at the NSCL. The only problem with this reaction is the difficulty in producing sufficiently intense and high-quality triton beams. At NSCL, tritons are produced as a secondary beam. The data presented here were taken using a 140 MeV/nucleon primary α beam impinging on a thick (9.25 g/cm2 ) Be target, producing 112 MeV/nucleon tritons with an intensity of ∼ 1 ·106 1/s. The 3 He ejectiles are momentum-analyzed in the S800 spectrometer. By employing the dispersionmatching technique, resolutions of about 160 keV have been achieved, although for the data discussed here, the resolution was somewhat worse (250 keV). For details of the method, see reference [14]. 2. Results A 7.6 mg/cm2 thick, 99.93% enriched 58 Ni target was used in the experiment. In addition, some data was taken with a CH2 target for calibration purposes. GT-strength in the spectra is identified using the angular distributions. Monopole transitions, like the GT, peak at θcm (t) = 0o . Dipole transitions peak at finite angle (θcm (t) ∼ 3o ). Higher multipoles have a flat angular distribution at forward angles and are suppressed at these
70c
R.G.T. Zegers et al. / Nuclear Physics A 758 (2005) 67c–70c
energies. Angular distributions up to 4o in the center-of-mass were measured. In Fig. 1 the preliminary results are shown. In (a), the measured cross section in the region below excitation energies of 10 MeV is shown in the angular range below 3o . The dominant peak in the spectrum is due to the 1+ state at 1.87 MeV. In (b), the differential cross section for foward (θcm (t) < 1o ) and finite (2o < θcm (t) < 3o ) angles are shown. Two main GT components in the spectra can readily be identified, as indicated in the figure, due to the unique foward-peaking angular distribution of L = 0 transitions. In order to extract the GT-strength over the full excitation-energy range, a multipole decomposition analysis (MDA) was performed. Three possible components (GT, dipole and a flat distribution mimicking contributions from higher multipole transitions) were assumed. The decompositions were performed per 0.4-MeV bin in excitation energy. Normalization of the data is still in progress and, for now, the B(GT) was normalized at the main 1+ state to the data from the 58 Ni(d,2 He) reaction [13]. For this particular target nucleus, the GT-strength distributions extracted from the 58 Ni(d,2 He) [13] and 58 Ni(n,p) [15] data show a clear discrepancy. The results presented here agree much better with the former: a strong peak at 1.87 MeV and concentrated strength near 4 MeV. The results from (n,p) display a broad GT-srength distribution between 1.5 and 5.5 MeV, and even if the limited resolution of 1 MeV is taken into account, this can not be matched with the results from (d,2 He) and (t,3 He). In the region between 5.5 MeV and 10 MeV, a rather flat and small GT distribution is found similar for the (n,p), (d,2 He) and (t,3 He) reactions. In conclusion, the results from the 58 Ni(t,3 He) experiment show that the (t,3 He) reaction at Et > 100 MeV is indeed a good probe to extract GT distributions. Over the last year, the triton beam has been further developed. Instead of using a primary α beam, a 150MeV/nucleon 16 O beam is used. A triton beam intensity of > 107 1/s can be obtained. The gain in intensity of a factor of 10 will ensure further improvement in the quality of the data sets. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
G.M.J. Fuller, W.A. Fowler and M.J. Newman, Astrophys. J. 293, 1. (1985). B.A. Brown and B.H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38, 29 (1988). T. Oda et al., At. Data Nucl. Data tables 56, 231 (1994). K. Langangke and G. Martinez-Pinedo, Nucl. Phys. A673, 481 (2000). E. Caurier et al., Nucl. Phys. A653, 439 (1999). A.K. Heger et al., Phys. Rev. Lett. 86, 1678 (2001). H.A. Bethe et al., Nucl. Phys. A324, 487 (1979). S.E. Koonin et al., Phys. Rep. 278, 2 (1995). K. Langanke et al., Phys. Rev. C 63, 032801 (2001). T.D. Taddeucci et al., Nucl. Phys. A469, 125 (1987). W.P. Alford and B.M. Spicer, Advances in Nuclear Physics, Vol. 24, 1 (1998). S.Rakers et al., Phys. Rev. C 65, 044323, (2002) M. Hagemann et al., Phys. Lett. B 579, 251 (2004). B.M. Sherrill et al., Nucl. Instrum. Methods Phys. Res. A432, 299 (1999). S. El-Kateb et al., Phys. Rev. C 49 (1994), 3128.
Weak interaction strengths for supernovae calculations via the (t,3 He) reaction on medium-heavy nuclei. R.G.T. Zegersa∗ A. L. Colea , H. Akimuneb , S.M. Austina , D. Bazina , A.M. van den Bergc , G.P.A. Bergc , J. Brownd , I. Daitoe , Y. Fujitaf , M. Fujiwarag , K. Harag , M.N. Harakehc , G.W. Hitta , M.E. Howardh , J. J¨aneckei , T. Kawabataj, T. Nakamurak , H. Uenol , H. Schatza , B.M. Sherrilla , M. Steinera a National Superconducting Cyclotron Laboratory, the Joint Institute for Nuclear Astrophysics and the Department of Physics, Michigan State University, MI 48824-1321, USA b c
Department of Physics, Konan University, Kobe, Hyogo 658-8501, Japan
Kernfysisch Versneller Insituut, Zernikelaan 25, 9747 AA Groningen, The Netherlands
d
Department of Physics, Wabash College, Crawfordsville, IN 47933, USA
e
Advanced Photon Research Center, Japan Atomic Research Institute, Kizu, Kyoto 619-0215, Japan
f
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
g
Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan
h
Physics Department, Ohio State University, Columbus, OH 43210, USA
i
Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
j
Center for Nuclear Study, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
k
Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 O-Okayama, Tokyo 152-8550, Japan l
Applied Nuclear Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan
The 58 Ni(t,3 He)58 Co reaction at 112 MeV/nucleon was measured to identify strength associated with Gamow-Teller transitions in the Tz = +1 direction. The experiment is a test case for future similar studies. The main aim of such studies is to test theoretical models used to predict Gamow-Teller strength distributions that serve as input for su∗
This work was supported by the US NSF (PHY02-16783, Joint Institute for Nuclear Astrophysics and PHY 0110253), The Ministry of Education, Science, Sports and Culture of Japan, the Stichting voor Fundamenteel Onderzoek der Materie (FOM), the Netherlands and by the Office of the Vice President for Research, University of Michigan.
0375-9474/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2005.05.018
68c
R.G.T. Zegers et al. / Nuclear Physics A 758 (2005) 67c–70c
pernovae evolution calculations. The results indicate that the (t,3 He) reaction is indeed a powerful tool to perform such tests. 1. Motivation In the later stages of stellar evolution, processes governed by the weak interaction determine the core entropy and electron to baryon ratio of the pre-supernova star. Electron capture (EC) reduces the number of electrons and beta decay works in the opposite direction. While Fermi transitions that play a role in beta decay are trivial to calculate, Gamow-Teller (GT) transitions (for both EC and beta decay) are difficult to predict. Initially, weak interaction rates by Fuller, Fowler and Newman (FFN) [1] based on an independent-particle model (IPM) were used for calculations with astrophysical purposes. However, the GT strength is strongly quenched and fragmented compared to IPM estimates due to residual interactions amongst the valence nucleons [2]. Hence, stellar weak interaction rates have been recalculated taking into account such effects for sd-shell nuclei [3] and pf-shell nuclei [4,5]. It was shown that these new estimates strongly affect the late evolution of stars [6] and that especially odd-N nuclei play an important role. When the collapse of the star occurs, a large fraction of the matter survives in heavy nuclei [7]. In describing the evolutionary path, EC is currently treated schematically: an IPM model is used in which GT transitions are Pauli blocked for nuclei with N>40 and Z<40 and do not provide EC strength. Again, due to residual interaction, this picture is too simple. Pauli unblocking can occur due to residual interactions. Moreover, because of the finite temperature in stars, further unblocking is possible. Shell-model calculations used for lighter nuclei are not yet feasible for these heavier nuclei and shell-model MonteCarlo calculations are used instead [8]. Such studies indicate that GT transitions are not fully Pauli blocked and dominate the EC process at stellar conditions since the number of available free protons is small compared to the number of heavier nuclei [9]. Because of these astrophysical applications, a push to measure GT transitions in mediumheavy nuclei (Fe-region) has been made. Different (n,p)-type reactions (∆Tz = +1) are used as a probe and all rely on the linear correlation between GT-strength [B(GT)] and the GT cross section at zero momentum transfer(q=0): dσ (q = 0) = KND | Jστ |2 B(GT ), (1) dΩ where K is a kinematical factor, ND the distortion factor and | Jστ |2 the volume integral of the nucleon-nucleus interaction. For the fundamental (p,n) charge-exchange reactions (and thus (n,p) as well), equation 1 has been tested in detail [10] and, except for a few cases, was found to be valid. Therefore, the (n,p) reaction seems to be the best probe to measure GT strength in the ∆Tz = +1 direction. Indeed, a fair amount of measurements have been performed [11]. However, due to the limited resolution (∼ 1 MeV) and the difficulty in producing intense neutron beams, the focus has shifted to other probes. The (d,2 He) reaction has been employed with good success (see e.g. [12,13]), due to the high resolutions obtained and the selectivity for spin-flip transitions. However, the reaction mechanism is complex since the ejectile is unbound. Also, the energy is somewhat low (85 MeV/nucleon) to ensure that linearity between cross section at q = 0 and B(GT) is maintained.
69c
R.G.T. Zegers et al. / Nuclear Physics A 758 (2005) 67c–70c
2
a)
dσ/dΩ (mb/sr)
1 0 3
3
58
Ni(t, He) Co Et=112 MeV/nucleon c) 0o-3o Result from MDA scaled to B(GT) 0.75 2 RY from (d, He) B(GT)
58
A
IN
b)
0oo-1oo 2 -3
GT
E PR
LIM 0.5
0.25
2 1 0
0
2.5
5
7.5 58
10
Ex( Co) (MeV)
0
0
2.5
5
7.5
10 58
Ex( Co)
Figure 1. Preliminary results for the 58 Ni(t,3 He)58 Co reaction at 112 MeV/nucleon: (a) differential cross section for θcm (t) < 3o . (b) same as (a), but for θcm (t) < 1o (full) and 2o < θcm (t) < 3o (dashed). Main components of the GT strength are indicated. (c) GTstrength extracted through MDA. The main GT-peak is at present scaled to the value obtained from the 58 Ni(d,2 He) reaction [13].
The (t,3 He) reaction at energies above 100 MeV/nucleon is an attractive alternative. The reaction mechanism is simple and can be tested in detail using the inverse reaction for which many data are available. The high energy ensures a strong preference for spinflip transitions and only minor contributions due to multi-step processes and the tensor-τ dσ component of the nucleon-nucleus interaction which break the B(GT)- dΩ (q = 0) linearity. Therefore, this probe has been developed at the NSCL. The only problem with this reaction is the difficulty in producing sufficiently intense and high-quality triton beams. At NSCL, tritons are produced as a secondary beam. The data presented here were taken using a 140 MeV/nucleon primary α beam impinging on a thick (9.25 g/cm2 ) Be target, producing 112 MeV/nucleon tritons with an intensity of ∼ 1 ·106 1/s. The 3 He ejectiles are momentum-analyzed in the S800 spectrometer. By employing the dispersionmatching technique, resolutions of about 160 keV have been achieved, although for the data discussed here, the resolution was somewhat worse (250 keV). For details of the method, see reference [14]. 2. Results A 7.6 mg/cm2 thick, 99.93% enriched 58 Ni target was used in the experiment. In addition, some data was taken with a CH2 target for calibration purposes. GT-strength in the spectra is identified using the angular distributions. Monopole transitions, like the GT, peak at θcm (t) = 0o . Dipole transitions peak at finite angle (θcm (t) ∼ 3o ). Higher multipoles have a flat angular distribution at forward angles and are suppressed at these
70c
R.G.T. Zegers et al. / Nuclear Physics A 758 (2005) 67c–70c
energies. Angular distributions up to 4o in the center-of-mass were measured. In Fig. 1 the preliminary results are shown. In (a), the measured cross section in the region below excitation energies of 10 MeV is shown in the angular range below 3o . The dominant peak in the spectrum is due to the 1+ state at 1.87 MeV. In (b), the differential cross section for foward (θcm (t) < 1o ) and finite (2o < θcm (t) < 3o ) angles are shown. Two main GT components in the spectra can readily be identified, as indicated in the figure, due to the unique foward-peaking angular distribution of L = 0 transitions. In order to extract the GT-strength over the full excitation-energy range, a multipole decomposition analysis (MDA) was performed. Three possible components (GT, dipole and a flat distribution mimicking contributions from higher multipole transitions) were assumed. The decompositions were performed per 0.4-MeV bin in excitation energy. Normalization of the data is still in progress and, for now, the B(GT) was normalized at the main 1+ state to the data from the 58 Ni(d,2 He) reaction [13]. For this particular target nucleus, the GT-strength distributions extracted from the 58 Ni(d,2 He) [13] and 58 Ni(n,p) [15] data show a clear discrepancy. The results presented here agree much better with the former: a strong peak at 1.87 MeV and concentrated strength near 4 MeV. The results from (n,p) display a broad GT-srength distribution between 1.5 and 5.5 MeV, and even if the limited resolution of 1 MeV is taken into account, this can not be matched with the results from (d,2 He) and (t,3 He). In the region between 5.5 MeV and 10 MeV, a rather flat and small GT distribution is found similar for the (n,p), (d,2 He) and (t,3 He) reactions. In conclusion, the results from the 58 Ni(t,3 He) experiment show that the (t,3 He) reaction at Et > 100 MeV is indeed a good probe to extract GT distributions. Over the last year, the triton beam has been further developed. Instead of using a primary α beam, a 150MeV/nucleon 16 O beam is used. A triton beam intensity of > 107 1/s can be obtained. The gain in intensity of a factor of 10 will ensure further improvement in the quality of the data sets. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
G.M.J. Fuller, W.A. Fowler and M.J. Newman, Astrophys. J. 293, 1. (1985). B.A. Brown and B.H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38, 29 (1988). T. Oda et al., At. Data Nucl. Data tables 56, 231 (1994). K. Langangke and G. Martinez-Pinedo, Nucl. Phys. A673, 481 (2000). E. Caurier et al., Nucl. Phys. A653, 439 (1999). A.K. Heger et al., Phys. Rev. Lett. 86, 1678 (2001). H.A. Bethe et al., Nucl. Phys. A324, 487 (1979). S.E. Koonin et al., Phys. Rep. 278, 2 (1995). K. Langanke et al., Phys. Rev. C 63, 032801 (2001). T.D. Taddeucci et al., Nucl. Phys. A469, 125 (1987). W.P. Alford and B.M. Spicer, Advances in Nuclear Physics, Vol. 24, 1 (1998). S.Rakers et al., Phys. Rev. C 65, 044323, (2002) M. Hagemann et al., Phys. Lett. B 579, 251 (2004). B.M. Sherrill et al., Nucl. Instrum. Methods Phys. Res. A432, 299 (1999). S. El-Kateb et al., Phys. Rev. C 49 (1994), 3128.