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$l$ -forbidden $\mathbf{M1}$ strengths near $^{100}$ Sn from knockout reactions in Cd and Sn

This study reports the measurement of hindered $l$ -forbidden M1 strengths in neutron-rich Cd and Sn nuclei near $^{100}$ Sn using knockout reactions and Doppler-shift lifetime measurements, revealing that current VS-IMSRG calculations systematically under-predict these transition strengths.

Original authors: T. J. Gray, K. L. Jones, R. Grzywacz, B. A. Brown, A. Gade, B. C. He, T. Miyagi, A. Peter, M. J. Basson, T. Beck, C. M. Campbell, G. Cerizza, J. Chung-Jung, I. Cox, P. Farris, R. Ghimire, S. Gillespie

Published 2026-07-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: T. J. Gray, K. L. Jones, R. Grzywacz, B. A. Brown, A. Gade, B. C. He, T. Miyagi, A. Peter, M. J. Basson, T. Beck, C. M. Campbell, G. Cerizza, J. Chung-Jung, I. Cox, P. Farris, R. Ghimire, S. Gillespie, M. Grinder, A. Hill, S. D. Pain, A. Palmisano-Kyle, K. P. Rykaczewski, D. Weisshaar, M. Williams

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the atomic nucleus not as a solid ball, but as a tiny, chaotic solar system. Inside this system, protons and neutrons (the "planets") orbit in specific lanes called shells. Usually, these planets stick to their assigned lanes. But sometimes, they get kicked out of their orbit or jump to a new one, and when they do, they emit a flash of energy (a gamma ray) to settle down.

This paper is about a team of scientists who acted like cosmic detectives, trying to figure out exactly how these particles behave when they make a very specific, difficult jump near a special "double-magic" nucleus called Tin-100 (100Sn).

Here is the story of their investigation, broken down simply:

1. The Setup: The Cosmic Cannonball

The scientists went to a massive machine called the Facility for Rare Isotope Beams (FRIB). Think of this as a giant cannon.

They fired a heavy beam of Xenon atoms at a target.
This collision shattered the atoms, creating a spray of new, unstable "isotope" fragments.
Among the debris, they caught a few rare, fast-moving atoms of Cadmium and Tin.
They then fired these fast atoms at a thin sheet of Beryllium (like a target in a shooting gallery).

2. The Reaction: The "Knockout"

When these fast atoms hit the Beryllium, it was like a game of billiards. The collision "knocked out" a single neutron from the Cadmium or Tin atoms.

The Result: The atom changed identity slightly (becoming a different isotope) and was left in an excited, wobbly state.
The Goal: The scientists wanted to watch how these wobbly atoms settled down. Specifically, they were looking for a very tricky move where a neutron jumps from one specific orbital lane to another.

3. The Mystery: The "Forbidden" Jump

In the world of nuclear physics, there are rules about how particles can move. Some moves are easy; others are "forbidden" (meaning they are very unlikely to happen).

The scientists were looking at a specific type of jump called an "l-forbidden M1 transition."
The Analogy: Imagine a dancer who is supposed to spin in place. An "allowed" move is a smooth spin. An "l-forbidden" move is like the dancer trying to spin while simultaneously hopping across the stage in a way that physics says they shouldn't be able to do easily.
Because this move is so difficult, it happens very slowly. The atom hangs out in its excited state for a tiny fraction of a second (about 400 picoseconds, or 0.0000000004 seconds) before finally making the jump and releasing a gamma ray.

4. The Measurement: The Doppler Effect

To measure this incredibly short pause, the scientists used a clever trick involving speed.

The atoms were moving at a significant fraction of the speed of light.
When a fast-moving object emits light (or gamma rays), the light gets squashed or stretched depending on the direction, similar to how a siren sounds higher as an ambulance approaches and lower as it drives away. This is the Doppler effect.
By looking at the "shape" of the gamma ray signal, the scientists could calculate exactly how long the atom waited before jumping.
The Finding: They measured these "wait times" for several new atoms (Cadmium-103, Cadmium-101, and Tin-103) and found they were indeed waiting a long time (relatively speaking) because the jump was so difficult.

5. The Conflict: Theory vs. Reality

This is where the paper gets interesting. The scientists took their new measurements and compared them to the best computer models available (called VS-IMSRG).

The Expectation: The computer models predicted that these "forbidden" jumps should be extremely rare, almost non-existent.
The Reality: The experiments showed that while the jumps are rare, they happen much more often than the computers predicted.
The Discrepancy: The computer models were "under-predicting" the strength of these jumps. It's like a weather forecast predicting a light drizzle, but the ground is actually soaked.

6. The Conclusion: We Need Better Rules

The paper concludes that our current "rulebook" for how these nuclear particles interact is missing something.

The scientists believe the computer models are missing a specific ingredient (related to how particles interact with each other in complex ways, specifically involving a particle state called the Delta isobar).
Without including this missing ingredient, the models cannot accurately predict how these "forbidden" jumps happen, even though they are good at predicting other things like the weight of the nucleus.

In Summary:
The team successfully caught rare atoms, measured how long they paused before making a difficult "forbidden" jump, and discovered that our best computer simulations are too pessimistic. The jumps happen more often than the math says they should, suggesting that our understanding of the fundamental rules of the atomic nucleus needs a little bit of an upgrade.

Technical Summary: $l$ -Forbidden M1 Strengths Near $^{100}$ Sn from Knockout Reactions in Cd and Sn

Problem and Motivation
Nuclear magnetic dipole moments serve as critical observables for understanding the microscopic properties of the atomic nucleus. While the nuclear shell model provides simple "Schmidt value" predictions for magnetic moments near closed shells, experimental values are frequently quenched. Explaining these deviations requires an effective M1 operator that accounts for core polarization, meson-exchange currents, isobar currents, and relativistic effects. A specific coupling term in this operator, the tensor term $g_P$ , is predominantly constrained by $l$ -forbidden M1 transitions (e.g., between the $0g_{7/2}$ and $1d_{5/2}$ orbits).

While empirical constraints on $g_P$ exist for lighter regions (such as the $sd$ and $pf$ shells), experimental data near the $^{100}$ Sn region—specifically involving the $0g_{7/2}$ and $1d_{5/2}$ neutron orbits—has been sparse. Furthermore, recent ab initio approaches, such as the Valence Space In Medium Similarity Renormalization Group (VS-IMSRG), have shown success in predicting ground-state magnetic moments but have not been rigorously tested against $l$ -forbidden M1 transition strengths in this mass region. This study addresses the lack of experimental constraints on $l$ -forbidden M1 strengths near $^{100}$ Sn to test the validity of current effective operators and ab initio calculations.

Methodology
The experiment was conducted at the Facility for Rare Isotope Beams (FRIB) using the S800 spectrograph and the GRETINA $\gamma$ -ray tracking array.

Beams and Targets: A primary beam of 227 MeV/nucleon $^{124}$ Xe was fragmented on a $^{12}$ C target. The Advanced Rare Isotope Separator (ARIS) delivered beams of $^{104,106}$ Sn. The study focused on neutron knockout reactions on contaminant beams of $^{104,102}$ Cd and the primary $^{104}$ Sn beam incident on a 9Be target.
Reaction Channels: The study analyzed one-neutron ( $1n$ ) and two-neutron ( $2n$ ) removal channels to populate residual nuclei $^{103,101}$ Cd and $^{103}$ Sn.
Particle Identification: Residue particle identification (PID) was performed event-by-event using the $\Delta E$ -TOF method at the S800 focal plane, gating on $\gamma$ -rays ( $E_\gamma > 100$ keV) to suppress unreacted beam components.
Lifetime Measurements: Excited-state half-lives were extracted by analyzing the Doppler-shifted lineshapes of $\gamma$ -ray transitions. The analysis utilized the UCGretina GEANT4 framework to simulate response functions, accounting for beam spot angles, target $z$ -offsets (optimized to 1.0 mm), and complex background shapes induced by neutrons.
Theoretical Comparison: Experimental results were compared with shell model calculations using the "jj45b" interaction and VS-IMSRG calculations using the 1.8/2.0 (EM) interaction. The VS-IMSRG calculations included both one-body currents (1BC) and one- plus two-body currents (1BC+2BC).

Key Contributions and Results
The paper presents the first direct reaction study of $^{103}$ Cd and provides new spectroscopic data for the exotic $^{101}$ Cd and $^{103}$ Sn nuclei.

New Spectroscopy: The level schemes for $^{103}$ Cd and $^{101}$ Cd were extended with 3 and 12 new $\gamma$ -ray transitions, respectively. Several transitions were observed with specific selectivity based on momentum transfer ( $\Delta p$ ) and $\gamma$ -ray multiplicity ( $\gamma_{mult}$ ).
Half-Life Measurements: Half-lives were measured for low-lying states with $\nu g_{7/2}$ $ν g_{7/2}$ character, which decay via $l$ $l$ -forbidden M1 transitions to $5/2^+$ $5/ 2^{+}$ states:
- $^{103}$ Cd: $T_{1/2}(188 \text{ keV}) = 410(95)$ ps; $T_{1/2}(2571 \text{ keV}) = 67(17)$ ps.
- $^{101}$ Cd: $T_{1/2}(252 \text{ keV}) = 230(30)$ ps.
- $^{103}$ Sn: $T_{1/2}(168 \text{ keV}) = 430^{+300}_{-220}$ ps.
B(M1) Strengths: These half-lives were converted into $B(M1; 7/2^+ \to 5/2^+)$ strengths. The values are small but non-zero, ranging from approximately $0.010$ to $0.017 \mu_N^2$ .
Theoretical Discrepancy:
- Shell model calculations using the "jj45b" interaction with an effective M1 operator (constrained by empirical $g_L$ and $g_S$ values and a tensor term $g_P \approx -2.3$ ) reproduced the experimental strengths reasonably well for $N < 56$ .
- However, VS-IMSRG calculations, even when including two-body currents, significantly under-predicted the $l$ -forbidden M1 strengths. The calculated strengths were effectively vanishing, similar to those obtained with the bare M1 operator. This discrepancy was observed not only in the $^{100}$ Sn region but also in other regions near double shell closures (e.g., $^{37}$ Cl, $^{39}$ K, $^{209}$ Bi).

Significance
The paper claims that the measured $l$ -forbidden M1 strengths provide a stringent new constraint on the effective M1 operator near $^{100}$ Sn. The results highlight a specific limitation in current ab initio approaches: while VS-IMSRG successfully describes ground-state magnetic moments, it fails to reproduce the magnitude of $l$ -forbidden M1 transition strengths. The authors suggest that this global under-prediction may stem from the omission of the $\Delta(1232)$ isobar state in the current VS-IMSRG formulation of the effective operator. Consequently, these experimental results motivate future theoretical work to incorporate such effects to achieve a more accurate first-principles description of nuclear M1 properties.