Quantum Few-Body Dynamics Group · Tongji University
The Big Bang produced hydrogen, helium and almost nothing else. Every heavier nucleus, in a rock, in the ocean, in your body, was assembled by a nuclear reaction inside a star, a supernova or a neutron star merger. We build the theory that says how those reactions proceed, and it is not yet as accurate as the observations demand.
大爆炸主要造出了氢和氦，其他元素极少。你身上更重的原子核，来自恒星、超新星或者中子星并合中的核反应。这些反应有多快、走哪条路，得靠理论算。我们算的就是这个，而且现在还算不够准。
Why this field为什么是这个领域
Cosmology wins on distance and on the age of the world, and we are not going to compete with it there. Nuclear physics has a different case to make, and it is a stronger one than the field usually bothers to state.
和宇宙学比距离、比时间跨度，核物理当然占不到便宜。原子核值得研究，理由在它自身。
A universe of hydrogen and helium has no chemistry, no rock, no biology. Everything that makes the universe interesting was manufactured at nuclear energy scales, and much of it is still being manufactured now, in objects we can observe but cannot reproduce. Cosmology builds the stage. Nuclear physics explains why anything is standing on it.
如果宇宙里只有氢和氦，化学会单调得多，也没有构成岩石和生命所需的碳、氧、硅、铁。恒星、超新星和中子星并合中的核反应造出了这些重元素，其中有些过程搬不进实验室。我们算的是这些反应走哪条路径、以多快的速度发生。宇宙学讲舞台是怎么搭起来的，核物理回答舞台上为什么会有东西。
Physics succeeds at the two ends. One end is one body and perturbation theory: atoms, QED, particle scattering, ten significant figures. The other end is the thermodynamic limit, where the law of large numbers takes over. The nucleus sits in between: tens to hundreds of strongly interacting particles, no small parameter, no large number, and an open system that can come apart while you look at it. That middle square is the shape of almost every hard problem left in science, and the nucleus is its model organism.
对相互作用较弱的少体系统，微扰展开很有效，原子和 QED 的结果能算到十位有效数字。粒子足够多时，又可以依靠统计平均和热力学。原子核正好卡在中间：几十到几百个粒子强烈作用，既没有明显的小量可供展开，也没有足够大的数目可供平均；碰撞中的原子核还会破裂，是一个会向外流失粒子的开放系统。它是研究这类有限强耦合多体问题的好对象，实验数据已经积累了六十年，也有多种算法可以互相核对。
Look outward and cosmology runs to 1026 m. Look inward and the sequence stops at 10−15 m, because below the nucleus quarks are confined and the notion of structure dissolves. The nucleus is therefore the last object one can still ask to have a shape, a rotation, a vibration. A few dozen particles manage to behave as a Fermi liquid, a superfluid, a rotating rigid body and a quantum chaotic system, sometimes within one isotope chain.
往外看，宇宙学能看到 1026 米。往里到 10−15 米，就进入了原子核的尺度。我们仍能把整个原子核的形变、转动和振动当作可测量对象；再往下研究夸克和胶子时，自由度和描述方式都变了，不能直接照搬这套形状语言。几十个核子组成的系统可以像液体、超流体或转动的刚体，也会出现量子混沌，有时这些现象就在同一条同位素链上依次出现。
No theory predicts all nuclei quantitatively. Roughly half the nuclei that models say should be bound have never been made. Nobody knows how heavy an element can get, what the interior of a neutron star is made of, or where most of the heavy elements were actually produced. A field in that state has room in it. That is the honest reason to work here rather than on a subject that was finished thirty years ago.
没有一套理论能把所有原子核都算准。模型认为应该能存在的核，大概有一半人类还没造出来过。元素最重能到哪里，中子星内部由什么组成，宇宙里大部分重元素究竟在哪里合成，这些基本问题都没有定论。新测量经常会迫使理论重算。
And it is the one branch of physics whose results went directly into the political history of the twentieth century, and whose next chapter is being written in energy. Work done here has consequences.
核物理的成果直接影响过二十世纪的政治史，如今又进入能源、医学和安全问题。做这类研究时，技术判断和社会后果离得很近。
What we work on我们做什么
We compute what happens when two nuclei collide. The projectiles we care about most are bound so weakly that they come apart during the collision, so the continuum has to be in the calculation from the start rather than added afterwards as a correction.
我们计算两个原子核碰撞后会发生什么，尤其关心束缚得很松的入射核。比如 6Li，可以近似看成一个 α 粒子和一个氘核松散地结合在一起，碰撞时很容易分开。分开后的碎片可能一个被靶核吸收，另一个继续飞走。物理上允许这些碎片逃逸的状态叫连续态，计算必须从一开始就把它们包括进去。
When a weakly bound projectile such as 6Li, 9Be or 11Be hits a target, only part of it may be captured. What gets measured is one fragment, and that measurement mixes elastic breakup with the events in which the other fragment is absorbed, excites the target, or is transferred. We separate the two in the Ichimura-Austern-Vincent model and its coupled-channel extensions, and use the separation to account for the suppression of complete fusion.
6Li 打在靶上，探测器常常只看到飞出来的那个 α 粒子。这个 α 有两个来源：6Li 散成 α 和氘核后，两个碎片都飞走；或者氘核被靶吸收，只剩 α 出来。后一类过程叫非弹性破裂，其中包括只吸收一部分入射核的不完全熔合。实验测到的截面把两类过程混在一起，我们用 Ichimura-Austern-Vincent 模型从理论上拆分它们，再研究弱束缚核的完全熔合截面为什么低于预期。
A calculation with imaginary potentials tells you how much flux is lost, not what it was lost to. We derive exact decompositions: how the absorbed flux divides between fusion and peripheral loss, and how to construct the Feshbach dynamic polarization potential while keeping the full continuum coupling, with no weak-coupling and no local-equivalent approximation.
反应计算常用带虚部的势记录有多少粒子没有以原样散射出去。这个记账办法只给出总损失，分不清粒子是真的进入靶核形成熔合，还是在靶核外围转入其他反应。我们推导严格的分解公式，还把破裂通道对弹性散射的影响压缩成一个等效势，并保留通道之间的全部耦合。
Bound-state techniques for scattering, complex scaling, Lagrange-mesh and R-matrix methods, GPU linear algebra, and reduced-basis emulators. The last of these reproduces a full continuum-discretized coupled-channel calculation to better than 0.1 percent at roughly two hundred times the speed.
上面这些计算一次常要几个小时。我们改进底层数值方法：用有限区域里的边界匹配处理散射，用复标度把远处不断振荡的波函数变成衰减函数，用 R 矩阵连接核内区和外区，再把最费时的线性代数搬到 GPU。降基代理则从几百个完整解里提取少数主要形状，用它们快速近似新的解。它能把完整计算复现到 0.1% 以内，速度快两百倍左右。
Optical potentials carry a dozen or more fitted parameters and the fits are ambiguous. We measure the ambiguity rather than assume it: Bayesian calibration with exact likelihood gradients, and Fisher-information geometry to count how many independent parameter directions a given data set constrains. The count is usually much smaller than the number of parameters being varied.
光学势有十几个拟合参数，不同的参数组合却能给出几乎一样的角分布。贝叶斯方法保留所有与数据相容的参数及其概率，不只报一组最优值。Fisher 信息几何再检查哪些参数只能一起变化、无法被数据分别识别，从而数出数据真正约束了几个独立方向。答案常常是两三个，而拟合里有十三个参数。
Networks enter for one of two reasons, differentiability or speed. Physics-informed networks solve the scattering problem once an exterior complex scaling boundary makes the asymptotic oscillation tractable. A bidirectional recurrent surrogate maps a global optical potential onto nucleon-nucleus scattering wave functions over 1 to 200 MeV, twelve target nuclei and partial waves up to l = 30, differentiable end to end.
我们只在神经网络能省计算时间或方便求导时使用它。物理信息神经网络直接用散射方程约束训练，但远处持续振荡的波函数很难学习；外部复标度把这段振荡转成衰减，同时保留实轴上的光学势。另一套网络学习光学势到波函数的映射，覆盖 1 到 200 MeV、十二个靶核，并能直接计算结果对输入参数的导数。
Software软件
Almost every result on this site came out of a solver written in the group. Most of them are on GitHub with the paper that documents them. A student who spends a few years here leaves with a code that runs, which is a more durable asset than a list of publications.
网站上几乎每个结果都来自组里自己写的程序，大部分随论文放到 GitHub。学生会从运行现有代码开始，逐步负责其中一个能独立检验、也能交给别人使用的部分。
General Julia scattering solver, Lagrange-Legendre basis with direct boundary matching, built to be emulated.
Julia 写的散射求解器，把无限远处的散射边界转成有限位置的直接匹配问题，也方便后续建立快速代理模型。
Complex-scaled optical and Coulomb scattering solver, local and Perey-Buck nonlocal potentials.
用复标度把振荡的散射波变成可积的衰减函数，再求解光学势和库仑散射；局域势和非局域势都能算。
Physics-informed neural network scattering solver with an exterior complex scaling boundary.
用散射方程约束神经网络训练，并靠外部复标度压下远处难以学习的振荡。
Production Fortran code for inclusive nonelastic breakup, DWBA and CDCC wave functions.
Fortran 写的非弹性破裂主程序，用来计算只探测一个碎片、另一个碎片被吸收或转移的反应。
Selected recent work近期工作选录
Join us加入我们
A first project here does not start with review articles. It starts with a real calculation: take a global optical potential, compute the elastic angular distribution for a real system, pull the measured points from the database and put them on the same plot. Two hours in, the diffraction minima either line up or they do not, and you have found out something about the world by computing it yourself. Very few fields can hand a second-year student that experience.
第一个课题会直接上手真实计算，不用先读三个月综述。你可以拿一个现成的光学势，计算某个核打在某个靶上的弹性散射角分布，再从数据库取出几十年前的实验点，画在同一张图上。一个下午之后，衍射极小可能对得上，也可能对不上。接下来就查单位、势参数和数值收敛，看看差别来自哪里。这些检查，大二学生已经能做。
Master’s and doctoral students are recruited every year. What we need is quantum mechanics at the level of a solid undergraduate course and a willingness to program; Fortran, Python and Julia are taught inside the group. What we do not need is prior nuclear physics.
硕士和博士每年都招。学过本科量子力学、愿意写程序就可以联系，不要求已有核物理基础。Fortran、Python、Julia 可以进组后学。
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