Mass spectrometry of $^{75}$Zn ground and isomeric states from in-trap decay of $^{75}$Cu

This paper reports the first direct mass spectrometry investigation of the ground and isomeric states of $^{75}$Zn using ISOLTRAP, which corrects the ground-state mass excess, confirms the isomer's excitation energy, and provides strong evidence for a spin-1/2 ground state that aligns with large-scale shell-model predictions.

The Gist

Imagine the atomic nucleus as a tiny, bustling city made of protons and neutrons. In this city, the "citizens" (particles) can live in different neighborhoods. Usually, they settle into the most comfortable, lowest-energy neighborhood, which we call the ground state. But sometimes, a citizen gets excited, jumps to a higher floor, and stays there for a while before falling back down. This excited version is called an isomer.

For a long time, scientists studying a specific atom called Zinc-75 ($^{75}\text{Zn}$) were confused. They knew the city existed, but they couldn't tell which citizen was the "Mayor" (the ground state) and which was the "Visiting VIP" (the isomer). They had two different measurements of the city's total weight, but they didn't know which weight belonged to which version of the city.

Here is what this new paper did to solve the mystery, explained simply:

1. The Problem: A Case of Mistaken Identity

Think of Zinc-75 like a pair of identical twins. One twin is the "Mayor" (ground state), and the other is the "VIP" (isomer).

• In 2005, scientists weighed the twins and said, "This is the Mayor!"
• In 2011, other scientists looked at how the twins decayed (changed) and said, "Wait, there's a VIP living 127 keV (a tiny bit of energy) higher up!"
• The problem? The 2005 weight measurement didn't match the VIP's weight perfectly, but it was close. Scientists were stuck wondering: Did we weigh the Mayor, or did we accidentally weigh the VIP and call it the Mayor?

2. The Solution: The "Trap and Wait" Strategy

To solve this, the team at CERN (the European nuclear research lab) used a clever trick. They didn't try to catch the Zinc twins directly because they are hard to make in large numbers. Instead, they caught the parent of the twins, a Copper atom ($^{75}\text{Cu}$), and put it in a special magnetic "trap."

Imagine putting a parent in a cage and waiting for them to have a baby.

• The Trap: They used a Penning trap, which is like a magnetic bowl that holds charged particles in place using magnetic and electric fields.
• The Wait: They let the Copper parent sit there for a few seconds. Eventually, the Copper parent naturally decayed (transformed) into Zinc.
• The Surprise: Because they waited, the Zinc "babies" were born in both states: some as the calm Mayor (ground state) and some as the excited VIP (isomer).

3. The Measurement: The "Magnetic Dance"

Once they had both versions of Zinc, they needed to weigh them with extreme precision. They used a technique called Time-of-Flight Ion Cyclotron Resonance (ToF-ICR).

Here is the analogy:
Imagine the atoms are dancers on a giant, invisible turntable (the magnetic field).

• Every dancer has a specific "spin speed" (frequency) that depends entirely on their weight. Heavier dancers spin slower; lighter dancers spin faster.
• The scientists gave the dancers a little nudge (a radio frequency pulse) to see if they would start dancing in sync.
• When the nudge matched the dancer's natural spin speed, the dancer's orbit got bigger, and they flew out of the trap faster.
• By measuring exactly how long it took them to fly out, the scientists could calculate their weight with incredible precision.

4. The Discovery: Who is the Mayor?

The results were a game-changer:

• The VIP Found: They successfully weighed the excited "VIP" state for the first time. It was sitting at an energy level of 123.7 keV, which matched the 2011 predictions perfectly.
• The Mayor Re-identified: They realized the 2005 measurement (which everyone thought was the Mayor) was actually the weight of the VIP!
• The New Truth: The real Mayor (the ground state) is actually lighter than previously thought. Its weight is now corrected to a new, more accurate number.

5. The Spin Mystery: A Puzzle for Theorists

In the world of atoms, "spin" is like how the atom is rotating. Scientists had to figure out: Does the Mayor spin fast (spin 7/2) or slow (spin 1/2)?

• The Clue: In previous experiments, they noticed that when making Zinc-75, they got way more of the "7/2 spin" version than the "1/2 spin" version (a 6-to-1 ratio).
• The Logic: If the 2005 experiment weighed the "7/2" version, and that version turned out to be the heavier one (the VIP), then the Mayor must be the "1/2" version.
• The Conflict: This is a headache for computer models. Most super-computer simulations predicted the Mayor should be the "5/2" or "9/2" spin, not "1/2". This paper suggests the computers need an update!

The Big Picture

This paper is like a detective story where the scientists:

1. Caught the parent to create the twins.
2. Weighed them separately using a magnetic dance floor.
3. Realized they had been misidentifying the twins for 20 years.
4. Corrected the record, proving the "Mayor" of Zinc-75 is actually a "1/2 spin" atom, not the one everyone thought.

This discovery helps physicists understand how the "city" of the atomic nucleus is built, especially near the "magic number" of 28 protons (Nickel), where the rules of nuclear structure get very strange and interesting. It's a small correction in weight, but a giant leap in understanding the universe's building blocks.

Technical Summary

1. Problem Statement

The zinc isotopic chain ($Z=30$) is critical for understanding nuclear structure evolution above the closed $Z=28$ (nickel) shell, particularly regarding the behavior of neutron orbitals near $N=40$. However, the nuclear structure of $^{75}$Zn ($N=45$) has been ambiguous due to conflicting experimental and theoretical data:

• Previous Mass Measurements: A 2005 study by Baruah et al. [6] measured the mass of a single long-lived state in $^{75}$Zn and assigned it to the ground state.
• Decay Spectroscopy: A 2011 study by Ilyushkin et al. [1] identified an isomeric state at 127.01(9) keV via $\beta$-decay of $^{75}$Cu, which was not observed in the earlier mass measurement.
• Spin-Parity Discrepancy: Laser spectroscopy and theoretical models (Shell Model, MCSM) offer conflicting assignments for the ground state spin ($1/2^-$, $5/2^+$, $7/2^+$, or $9/2^+$).
• The Core Issue: It was unclear whether the mass measured in 2005 corresponded to the true ground state or the isomer, and the spin-parity ordering of the $1/2$ and $7/2$ states remained unresolved.

2. Methodology

The authors utilized the ISOLTRAP Penning-trap mass spectrometer at ISOLDE/CERN to perform high-precision mass measurements.

• Ion Production & In-Trap Decay:

  • Instead of producing $^{75}$Zn directly from the fission target (which yields insufficient quantities of the specific state), the team produced the parent nucleus $^{75}$Cu via neutron-induced fission of uranium.
  • $^{75}$Cu ions were purified and trapped in the Preparation Penning Trap.
  • An extended cooling time (1–9 seconds) was applied to allow the majority of $^{75}$Cu to undergo in-trap $\beta$-decay, populating both the ground and isomeric states of $^{75}$Zn.
  • Mass-Selective Buffer Gas Cooling was employed to remove residual $^{75}$Cu ions, ensuring only $^{75}$Zn ions were transferred to the measurement trap.

• Measurement Technique:

  • Time-of-Flight Ion-Cyclotron-Resonance (ToF-ICR): The cyclotron frequency ($\nu_c$) of the ions was measured in a 5.9 T magnetic field.
  • Reference Ions: $^{85}$Rb$^+$ and $^{133}$Cs$^+$ from an offline ion source were used to calibrate the magnetic field and determine the mass ratio.
  • Data Analysis: The "z-class" analysis method was used to correct for systematic shifts caused by ion-ion interactions, extrapolating results to a single-ion limit.

• Theoretical Calculations:

  • The authors performed Skyrme Hartree-Fock plus Bardeen-Cooper-Schrieffer (HF-BCS) calculations to predict the ground-state spin and parity of $^{75}$Zn, comparing these with Large-Scale Shell Model (LSSM) and Monte Carlo Shell Model (MCSM) predictions.

3. Key Contributions

• First Direct Mass Spectrometry of the Isomer: This is the first time the isomeric state of $^{75}$Zn has been directly investigated via mass spectrometry, distinct from the ground state.
• Correction of Ground-State Mass: The study identified that the 2005 measurement by Baruah et al. actually measured the isomeric state, not the ground state. Consequently, the ground-state mass excess was revised.
• Spin-Parity Resolution: By combining new mass data with production ratios from laser spectroscopy and theoretical modeling, the authors provide strong evidence for a $1/2^-$ ground state, challenging previous assumptions.

4. Results

A. Mass Measurements

• Isomeric State ($^{75m}$Zn): Measured at an excitation energy of 123.7(20) keV. This is in $2\sigma$ agreement with the value derived from decay spectroscopy (127.01 keV).
• Ground State ($^{75}$Zn): The mass excess was determined to be $-62,681.0(21)$ keV.
  • Significance: The previous value ($-62,558.9$ keV) from [6] is now understood to be the mass of the isomer. The new ground-state mass is approximately 122 keV lower than the previously accepted value.

B. Branching Ratios and Half-Lives

• The ratio of isomeric to ground state production ($N_m / (N_g + N_m)$) increased from 0.60(7) at 1s storage to 0.74(3) at 9s storage.
• This shift implies the isomer has a half-life longer than 5 seconds (and likely longer than the ground state), though limited statistics prevented a definitive half-life determination.

C. Two-Neutron Separation Energy ($S_{2n}$)

• Incorporating the corrected ground-state mass of $^{75}$Zn smooths the downward linear trend of $S_{2n}$ for Zinc isotopes, resolving previous irregularities in the nuclear binding energy systematics near $N=45$ and $N=47$.

D. Spin-Parity Assignment

• Production Ratio Argument: Laser spectroscopy at ISOLDE showed a production ratio of $7/2 : 1/2$ states of 6:1. Since the 2005 mass measurement (now identified as the isomer) corresponds to the more abundant state, the $7/2$ state is the isomer.
• Conclusion: The ground state must be $1/2^-$.
• Theoretical Consistency:
  • The authors' HF-BCS calculations consistently predict a $5/2^+$ ground state (disagreeing with the $1/2^-$ conclusion).
  • However, the MCSM with LNPS-m interaction predicts a $1/2^-$ ground state, which aligns with the experimental evidence presented here.
  • The JUN45 and A3DA-m interactions predict $9/2^+$ and $5/2^+$ respectively, failing to match the experimental data.

5. Significance

• Nuclear Structure Models: The results highlight significant discrepancies in current theoretical models (Shell Model and MCSM) regarding the ground-state spin of $^{75}$Zn. The experimental evidence for a $1/2^-$ ground state challenges models that predict $5/2^+$ or $9/2^+$, suggesting that specific effective interactions (like LNPS-m) or pairing strengths need refinement.
• Isomeric Identification: The study demonstrates the power of in-trap decay combined with Penning-trap mass spectrometry to resolve ambiguities between ground and isomeric states that are indistinguishable in standard production methods.
• Systematics: The corrected mass values provide a more accurate baseline for calculating two-neutron separation energies, crucial for understanding the evolution of nuclear shapes and shell closures in the $N \approx 40$ region.

Conclusion: The paper successfully redefines the mass and spin-parity landscape of $^{75}$Zn, proving that the previously measured "ground state" was actually an isomer, and providing compelling evidence that the true ground state has a spin-parity of $1/2^-$.