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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Atomic Spectroscopy: Effects of Temperature01:27

Atomic Spectroscopy: Effects of Temperature

Atomization, converting samples into gas-phase atoms and ions, is essential for atomic spectroscopy. The flame temperature required for atomization affects the efficiency of the atomic spectroscopic methods by increasing the atomization efficiency and the relative population of the excited and ground states.
At thermal equilibrium, the relative populations of excited and ground state atoms can be estimated using the Maxwell–Boltzmann distribution. For example, an increase in temperature from...
Nuclear Stability03:18

Nuclear Stability

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
To hold positively charged protons together in the...
Radioactivity and Nuclear Equations03:18

Radioactivity and Nuclear Equations

Nuclear chemistry is the study of reactions that involve changes in nuclear structure. The nucleus of an atom is composed of protons and, except for hydrogen, neutrons. The number of protons in the nucleus is called the atomic number (Z) of the element, and the sum of the number of protons and the number of neutrons is the mass number (A). Atoms with the same atomic number but different mass numbers are isotopes of the same element.
A nuclide of an element has a specific number of protons and...
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...

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Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Low-temperature triple-alpha rate in a full three-body nuclear model.

N B Nguyen1, F M Nunes, I J Thompson

  • 1National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA. nguyenn@nscl.msu.edu

Physical Review Letters
|October 23, 2012
PubMed
Summary

A new three-body method accurately calculates the triple-alpha capture reaction rate, crucial for carbon production in stars. It reveals a significant rate enhancement at low temperatures, impacting stellar evolution models.

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Last Updated: May 17, 2026

Setting Limits on Supersymmetry Using Simplified Models
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Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis
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Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis

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Area of Science:

  • Nuclear Astrophysics
  • Stellar Evolution
  • Computational Physics

Background:

  • The triple-alpha capture reaction is the primary source of carbon-12 (12C) in stars.
  • Accurate reaction rates are essential for understanding stellar nucleosynthesis and evolution.
  • Previous calculations involved approximations that may affect low-temperature rate predictions.

Purpose of the Study:

  • To compute the triple-alpha capture reaction rate using a novel three-body method.
  • To investigate the impact of pairwise Coulomb interactions on the reaction continuum.
  • To compare the new rate with existing compilations and assess its effect on stellar models.

Main Methods:

  • Developed a new three-body method combining Faddeev hyperspherical harmonics and the R-matrix method.
  • Obtained a full solution for the three-body alpha+alpha+alpha continuum.
  • Specifically addressed long-range effects from pairwise Coulomb interactions.

Main Results:

  • The new triple-alpha reaction rate agrees with existing compilations for temperatures above 0.07 GK.
  • A significant enhancement (≈10^12) of the reaction rate was found at lower temperatures (0.02 GK).
  • The updated rate does not substantially alter the evolution of one-solar-mass stars, including their red-giant phase and white dwarf remnants.

Conclusions:

  • The novel three-body method provides a more accurate triple-alpha reaction rate, especially at low temperatures.
  • Despite the low-temperature enhancement, the overall evolution of Sun-like stars remains consistent with observations.
  • The study validates current understanding of red-giant phases and white dwarf formation in solar-mass stars.