Photodisintegration reaction measurement: a probe of p-process for nuclear astrophysics ● Introduction ● Photodisintegration ● Experimental methods ● Works by Beihang group Liuchun He, Bao-Hua Sun, Li-Hua Zhu, Jian-Wei Zhao, Meng Wang, Kang Wang School of Physics and Nuclear Energy Engineering, Beihang University

Introduction γ-process in massive stars p-process “g-process” r-process “rapid process” via unstable neutron-rich nuclei Neutron dripline (edge nuclear stablility) 对于稳定的核素，它们的比结合能在56Fe处达到了最大值[3,4]，铁以上的元素不能再通过类似氢燃烧，氦燃烧[1]等方式随恒星的演变熔合产生，并且随着元素质子数的增加，原子核内越来越大的库伦位垒导致了带电粒子的俘获反应越来越困难，此时，中性粒子的俘获反应开始起主导作用。各种模型研究表明，元素中的大部分（约99％）原子核主要是通过慢中子俘获过程（s-过程: slow neutron-capture process）[5,6]和快中子俘获过程（r-过程: rapid neutron-capture process）[7]来合成的。 然而，还有一些天然存在的丰质子同位素不在这些中子俘获过程的路径上，它们无法通过s-过程或r-过程来合成，这些元素被称为 p-原子核，如图 1中的156,158Dy、162,164Er和168Yb等。核素图上从元素硒(Se)到汞(Hg)的质量区域，大约30多个这样的 p-原子核[8-10]。与其它稳定同位素相比，p-原子核含有的中子 数较少，与通过s-过程和r-过程产生的同位素相比，它们的同位素丰度和太阳系丰度都极低，见图2。产生它们的天体环境、核合成机制都还不清楚，与其相关的核反应数据也非常缺乏，是当前天体物理核合成研究的重要热点问题之一。 在 II 型超新星[11,12]和Ia型超新星[13]中发生的γ-过程（光 致蜕变反应），热核燃烧期间中子星表面发生的rp-过程（质子俘获反应）[14]，或中微子驱动II型超新星的νp-过程(中微子俘获反应)[14]，等等。 为了使反应能在恒星演化的时间尺度上发生，温度一般不能低于1.5×109开尔文，而为了保证重元素不会被大量的光致裂变反应而过度侵蚀，一般也不能超过3.5×109开尔文。这样就给p-过程提供三种限制条件：足够丰度的种子核，足够高的温度，以及时间尺度足够短的热过程。 About 99% of the heavy elements are produced during the s and r processes However, a small fraction of neutron-deficient nuclei are bypassed by these neutron-capture processes. The approximately 35 proton-rich nuclei in the mass region between Se (Selenium [səˈlēnēəm]) and Hg (Mercury [ˈmərkyərē]) are believed to be produced by a variety of different processes, usually summarized as the p process. Among others, astrophysical processes producing the p nuclei are the γ process in type II supernovae and type Ia supernovae, the rp process during thermonuclear burning on a neutron-star surface, or the νp process in neutrino driven winds of type II supernovae. Lighter p nuclei are also efficiently produced in type Ia supernoave.

Introduction Typical parameters for γ-process: 2≤ 𝑇 9 （109𝐾）≤3, time scales 𝜏 in the order of seconds. Astrophysical sites not concluded: Oxygen- and neon-rich layers of type II supernovae in massive stars Woosley && Howard, APJS36, 285(1978) Rayet, Prantzos, Arnould, AA 22, 271 (1990). ~ 2000 isotopes ~ 20000 reactions (mainly unstable nuclei) Not possible to measure all the reaction rates in the laboratory. Statistical Hauser-Feshbach model Rare experiment data at A>130 II型超新星爆发中的富氢壳层可能是p-过程发生的地点，这也是恒星演化的最后阶段[12]。 为了使反应能在恒星演化的时间尺度上发生，温度一般不能低于1.5×109开尔文，而为了保证重元素不会被大量的光致裂变反应而过度侵蚀，一般也不能超过3.5×109开尔文。这样就给p-过程提供三种限制条件：足够丰度的种子核，足够高的温度，以及时间尺度足够短的热过程。 为了解决 p-原子核的起源之谜，必须将天体物理和核物理方面的研究与各种来自恒星光谱、陨石样品和核实验的大量“观测”信息相结合，将核天体物理模型与天文观测进行比较。p-过程主要涵盖了大量的光致裂变反应(γ,n)、(γ,p)、(γ,α)，也涉及了一部分的质子，中子，α粒子的俘获反应，且它们的质心能量应该远小于1MeV或者小于对应带电核的库仑位垒；而一部分弱相互作用，如β衰变、正负电子俘获、（反）中微子俘获也可能在特定情况下参与到p-过程中。为此，要对p-过程建立系统的可靠的网络方程模型进行计算，则需要同时考虑到质量数A≤210的约2000个核素相关的20000个反应，且主要涉及不稳定原子核的反应数据[17]。 实验上获得天体物理核合成网络中的所有原子核的反应数据是不可能的。其原因除了涉及不稳定核外，还有天体环境对应的能量较低，在较低能量下的核反应截面一般都非常低，实验本身有很大的困难。因此，天体物理对应能量的核反应实验数据一般很少，而关于p-原子核的实验数据就更加稀少。 Up to current knowledge, the majority of the p nuclei are produced by photodisintegration reactions during the γ process within O/Ne burning layers of core-collapse supernovae. When the shock-front passes the O/Ne (Neon) layer, temperatures of 2 GK T 3.5 GK are reached, allowing the partial photodisintegration of preexisting seed nuclei. The γ –process starts with sequences of (γ ,n) reactions. At some point, the (γ ,n) reactions will start to compete with (γ ,p) and (γ ,α) reactions as well as β decays, leading to deflections in the γ -process path. The reaction rates in the γ –process reaction network, which includes thousands of reactions on mainly unstable nuclei, are calculated within the scope of the Hauser-Feshbach (HF) statistical model. In order to obtain reliable model predictions, it is important to put the nuclear-physics input parameters entering these calculations on a firm basis. These nuclear-physics input parameters include nuclear level densities and γ -ray strength functions, which determine the γ width. Moreover, the particle+nucleus optical-model potentials (OMP) are needed to describe the particle widths for protons, neutrons, and α-particles. These parameters can, to some extent, be experimentally tested by laboratory experiments.

Photodisintegration The energy distribution of a thermal photon bath at a temperature T is given by the Planck distribution 700 349 140 Number of -rays at energy E per unit of volume and energy interval In a photon-induced reaction B(,x) A, the distribution leads to a temperature dependent decay rate T) of the initial nucleus B: Cross section of the -induced reaction -flux threshold The larger threshold energy, the smaller T) 3+𝛾→0+1 or 3+𝛾→4+5

At temperature of astrophysical interests Utsunomiya et al., NPA 2006 1-2 MeV Gamow window for (,n) (left panel) and () reactions (right panel) on the ground state of the target nucleus 148Gd. Note the temperature dependence of the position of the Gamow window when the emitted particle is charged as well as the significant changes of the vertical scales in both panels when T9 goes from 2 to 3.

Suggestions for reactions to be studied experimentally A well-known deficiency in the model is the underproduction of the Mo-Ru region, but the region 151 A 167 is also underproduced, even in recent calculations [3]. In this work the sensitivity of the location of the γ process path to reaction rates is investigated, showing which nuclei should be preferred in experimental studies. 表左：产率具有较大误差的核素，下角标表示与（g,n）反应产率接近的反应。 表右：优先进行实验研究的核素。 Thomas Rauscher, PRC, 73, 015804 (2006)

Quasi-monochromatic γ-rays Experiment method Direct determination of reaction rates Bremsstrahlung-induced activation Physics Reports 384 (2003) 1–84_3 Continuous energy distribution photons Superposition method Approximate satisfactorily a black-body Planck spectrum Laser Compton backscattering PHYSICAL REVIEW C 67, 015807 (2003) Quasi-monochromatic γ-rays

Detectors for (γ,X) BF3 3He Time Projection Chamber： Silicon detector： Neutron detectors： BF3 3He liquid scintillating detectors Li-loaded glass detectors

Experiment method (Inverse reactions ) Inverse reactions (p, g), (n, g), (a, g) Activation method：A (x, g) B  Radioactive γ-rays measurements Suitable T1/2 of B Low background In beam measurements: A (x, g) B  in-beam γ-rays measurements High detector efficiency

Experimental setup @ CIAE Beam : 3.4 MeV proton Target: #1 𝒏𝒂𝒕 𝑫𝒚 (𝟏.𝟗𝟐𝒎𝒈/𝒄 𝒎 𝟐 ) #2 𝒏𝒂𝒕 𝑫𝒚 (𝟏.𝟕𝟔𝒎𝒈/𝒄 𝒎 𝟐 ) #3 𝟏𝟔𝟎 𝑫𝒚 (𝟏.𝟖𝟓𝒎𝒈/𝒄 𝒎 𝟐 ) +𝟏𝟗𝟕 𝑨𝒖 (𝟑.𝟓𝟕𝒎𝒈/𝒄 𝒎 𝟐 ) natDy target: 156Dy(0.06%), 158Dy(0.1%), 160Dy(2.34%), 161Dy(18.91%), 162Dy(25.51%), 163Dy(24.90%), 164Dy(28.18%) 160Dy target: 160Dy(51.82%), 161Dy(13.87%), 162Dy(5.79%), 163Dy(3.05%), 164Dy(1.68%), O(17.6%). 改表格 Target Beam time Waiting time Measured time #1 41min 41s 10min 18s 55min 11s #2 40min 36s 7min 20s 1h 05min 13s #3 37min 54s 12min 16s 15h 21min 37s

Experimental setup @ CIAE HPGe detector with 105% relative efficiency, Source is 22.1 mm away from the detector surface. Background: 0.1/s

Correction for summing coincidence with Geant4 L.-C. He et al., Nucl. Instrum. Methods Phys. Res. A 880 (2018) 22–27

Spectrum: p + natDy Element abundance： Lifetime of production： 161Ho 2.48 (5) h 161mHo 6.76 (7) s 162Ho 15.0 (10) m 162mHo 67.0 (7) m 163Ho 4570 (25) y 163mHo 1.09 (3) s 164Ho 29 (1) m 164mHo 37.5 (15) m

Spectrum: p + 160Dy 103keV is the only 𝜸 ray visible from 161Ho with branching ratio of 3.9% Element abundance： 160Dy(51.82%), 161Dy(13.87%), 162Dy(5.79%), 163Dy(3.05%), 164Dy(1.68%), O(17.6%).

Contaminations in target p + natDy Lifetime of 511keV: 109.71 min Talys calculation: p + natO 𝟑.𝟒 𝑴𝒆𝑽 18F 2.272 × 10-1 mb p + 160Dy 𝟑.𝟒 𝑴𝒆𝑽 161Dy 3.665 × 10-3 mb Total 𝜷+ intensity: 96.73 %

Contaminations in target p + 160Dy

Contaminations in target Energy-dispersive X-ray spectroscopy Ge  71As 73As 74As 76As Zr  95Nb 96Nb 97Nb Mo  93Tc 95Tc O  18F Ca  48Sc Fe  55Co 58Co Cu  65Zn Zn  65Ga 70Ga The abundances of contamination elements are < 1% except O.

Preliminary Preliminary result Present work 162𝐸𝑟 𝑝,𝛾 163𝑇𝑚 162𝐸𝑟 𝑝,𝑛 162𝑇𝑚 N. Özkan, et al., Phys. Rev. C 96, 045805 (2017) Preliminary Prospect: Obtain more experimental data to cover the Gamow window (𝟒±𝟏 MeV) for Dy isotopes!

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