RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-1. Nuclear Physics

Investigation of the waiting point 22Mg in the rp-process
N. N. Duy,＊1, *2 L. H. Khiem,＊2 S. Kubono,＊3 H. Yamaguchi,＊4 D. Kahl,＊4 and N. K. Uyen*5
Nucleosynthesis in stars occurs via several reaction
chains, including a combination of the (α,p)-process,(p,γ)-process, and β+-decay. A nucleus is a waiting point ifthe (,p) or (p,γ) reaction rate is so low that the nuclear
processing has to wait for β+-decay. Since thenucleosynthesis grows to the 22Mg nucleus via thefollowing reaction chains, 14O(,p)(p,)18Ne(,p)(p,)22Mg(,p)(p,)26Si(,p)(p,)30S(,p)(p,)34Ar(,p)(p,)38K, there
are three possible ways by which the reactions can proceed
through 22Mg: 22Mg(β+)22Na, 22Mg(α,p)25Al, and22Mg(p,γ)23Al. Because of the small Q-value (Q = 0.125
MeV) of the (p,γ)-reaction, it is thought that thephotodisintergration of 23Al prevents a significant part of
the flow through this reaction. In addition, athigh-temperature condition, i.e., T 9 = 1 – 10 GK, the22Mg(α,p)25Al reaction was thought to be dominant. If thereaction rate of 22Mg(α,p)25Al is lower than the rate of beta
decay, the nucleosynthesis must await the decay from 22Mg,
and subsequently, the 22Mg nucleus becomes a waiting point.
To investigate the potential waiting of 22Mg, we measured
the 22Mg+ reaction and determined the resonance states1)of 26Si that are used to calculate the reaction rate of22Mg(,p)25Al under such stellar conditions. According tothe results of a previous work,2) we could estimate the rateof the (α,p)-process, (p,γ)-process, and β+-decay in 22Mg.
The reaction rate of 22Mg(,p)25Al was determined byusing the resonance states of 26Si obtained from alphascattering in the 22Mg+ experiment. The calculation wasperformed by using following expression:
N A  v8.08  109  T6 tot

3/ 2

 11605Ei  (1)T6   exp  ii

where , (), Ei, and T6 are reduced mass, resonancestrength, resonance states, and temperature in million
Kelvin, respectively. The resonance strength was calculated
by assuming that of the proton occupied 10% of the totalwidth. As shown in Fig. 1, the rates of the (α,p) reaction
corresponding to the first resonance is the highest. The
reaction rate is low under concerned stellar conditions, witha value in the range of 10-30 – 10-7. The speed of the (α,p)
reaction, which depends on the abundance of isotopes in thestellar environment, and that of beta decay were obtained
from the following equations:R p  XmR   ln 2 / T1/ 2 ,NA v pwhere , Xa, NA<v>, ma, and T1/2 are the density of thematerials in the stellar environment, abundance of 4He, rateof the (α,p) reaction, mass of 4He, and half-life of 22Mg.
According to the rates obtained in the previous work, 2) wecould determine the speed of the (p,γ) reaction. The results
show that in the temperature range of T 9 = 1 – 10 GK, the(p,γ) reaction is the dominant. Table 1 compares the threeprocesses.

Fig. 1. Rates of the reaction 22Mg(,p)25Al calculated byusing the resonance states of 26Si via alpha scattering of22Mg.
Table 1. Speed of the reactions and beta decay
T9(GK)
1.0
1.5
2.0
2.5
10Rp(reaction/s)
2.99E-06
1.79E-04
1.26E-03
3.90E-03
7.50E-02

Rp(reaction/s)
7.80E+03
2.47E+04
4.92E+04
7.80E+04----R +(decay/s)
0.17890.17890.17890.17890.1789Since the speed of the (p,γ) reaction is much higher thanthat of the others, it does not wait for beta decay. Therefore,
under the conditions of X-ray burst and Type-II supernovae,
the 22Mg nucleus does not act as a waiting point.
Subsequently, beta decay does not occur. Once the beta
decay is skipped, the 22Na unstable isotope which decays
beta-plus (+) to the excited state of 22Ne, which de-excites
to ground state by emitting gamma rays with energy of
1.275 MeV, cannot be formed. Therefore, such gamma rays
have not been observed by satellites up to date. In addition,
the 22Ne/20Ne ratio changes, which is one of the causes of
the Ne-E problem.

(2)
(3) 

Department of Physics, Dong Nai University.
Institute of Physics, Vietnam Academy of Science and Technology.
＊3
RIKEN Nishina Center.
＊4
Center for Nuclear Study, The University of Tokyo.
＊5
Department of Physics, HCM University of Technology and Education.
＊1＊2References

1) N. N. Duy et al: RIKEN Accel. Prog. Rep. 47, 43 (2015).
2) J. J. He et al: Phys. Rev. C 76, 1 (2007).

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