| name | gamma-selection-rules |
| description | Use this skill when deducing multipolarities for gamma transitions and then Jπ for nuclear levels by combining constraints from feeding and deexciting gamma transitions using electromagnetic selection rules. Applies D/E2 rules to primary capture transitions, D/Q or D/E2 to deexciting gammas (if RUL applies), and takes AND intersection of all constraints. Handles multi-valued initial Jπ via union before intersection.
|
Gamma Transition Selection Rules: Deducing multipolarities and Jπ
- ENSDF 80-column data record and field definitions, structural rules, column positions, and uncertainty notation:
.github/agents/ENSDF-Agent.agent.md.
- Spot-check policy:
.github/copilot-instructions.md.
- γ-ray multipolarity selection rules:
.github/docs/gamma_selection_rules.md.
Goal
Deduce the multipolarity of γ-ray transitions from experimental data.
Deduce the Jπ of levels by combining constraints from:
- Feeding transitions — γ rays populating the level (from capture resonances above)
- Deexciting transitions — γ rays depopulating the level (to lower levels below)
Multipolarity Assignment Reasoning Logic in Individual Datasets
Scenario A: Only Mixing Ratios and Spins Given in Literature
- If level scheme indicates $\Delta J = 0$ or $1$, assign D+Q in M field.
- If level scheme indicates $\Delta J = 2$, assign Q+O in M field.
- If level scheme indicates $\Delta J = 3$, assign O in M field and note O+H and $\delta$ value in cG M,MR comment.
Scenario B: DCO Ratios, Mixing Ratio, and Spins Given in Literature
Step 1: Look at DCO Ratios
DCO Reference Gates
- Gating on a stretched dipole ($\Delta J = 1$) transition yields $R_{DCO}(D)$.
- Gating on a stretched quadrupole ($\Delta J = 2$) transition yields $R_{DCO}(Q)$.
- Expected DCO values depend on experimental detection setups. The values below are for example purposes.
DCO Decision Rules
If $R_{DCO}(D) \approx 1.0$ or $R_{DCO}(Q) \approx 0.5$:
- Transition is stretched dipole ($\Delta J = 1$) dominant.
- Mark as D.
If $R_{DCO}(Q) \approx 1.0$ or $R_{DCO}(D) \approx 2.0$:
- Transition is stretched quadrupole ($\Delta J = 2$) dominant and with a possibly weaker dipole or octupole component.
- Mark as Q.
- Then look at spins, a less common case is if the level scheme indicates $J_i = J_f$:
- Mark as ΔJ=0.
If $R_{DCO}$ is between two expected values or inconsistent with all expected values:
Step 2: Look at Mixing Ratio ($\delta$) and Level Scheme Spin Change ($\Delta J$)
Based on the Step 1 classification:
For Transitions Marked D
- If $\delta$ is not given, assign D in M field.
- If $|\delta| < 1$ is given, assign D+Q in M field.
For Transitions Marked Q
- If $\delta$ is not given, assign Q in M field.
- If $|\delta| < 1$ is given, assign Q+O in M field.
- Then look at spins, the level scheme should indicate $\Delta J = 2$; but if it indicates $\Delta J = 1$, assign D+Q in M field and flag this discrepancy for user review.
- If $|\delta| > 1$ is given, assign D+Q in M field because dipole is the weaker component.
For Transitions Marked ΔJ=0
- If $\delta$ is not given, assign D in M field and note "consistent with |DJ=0" in the cG comment after the DCO value.
- If $|\delta| < 1$ is given, assign D+Q in M field and note "consistent with |DJ=0" in the cG comment after the DCO value.
For Transitions Marked Mixed
- If $\delta$ is not given, no need to assign M field.
- If $\delta$ is given:
- If level scheme indicates $\Delta J = 0$ or $1$, assign D+Q in M field.
- If level scheme indicates $\Delta J = 2$, assign Q+O in M field.
- If level scheme indicates $\Delta J = 3$, assign O in M field and note O+H and $\delta$ value in cG M,MR comment.
Step 3: Mixing Ratio Refinement
- If $\delta$ is given and does not overlap with 0, D+Q or Q+O remains unchanged.
- If $\delta$ is given and overlaps with 0, place the higher-order multipolarity in parentheses:
- D+Q changes to D(+Q).
- Q+O changes to Q(+O).
Step 4: Polarization Refinement
Apply these rules based on measured POL to assign electromagnetic character:
Positive POL (Dominant Electric Character)
- D → E1
- Q → E2
- D+Q → E1+M2
- D(+Q) → E1(+M2)
- Q+O → E2+M3
- Q(+O) → E2(+M3)
Negative POL (Dominant Magnetic Character)
- D → M1
- Q → M2
- D+Q → M1+E2
- D(+Q) → M1(+E2)
- Q+O → M2+E3
- Q(+O) → M2(+E3)
If No POL Data Available
- Do not assign E or M labels.
- Assign only D, Q, O multipolarities based on DCO decision rules above.
Multipolarity Assignment Reasoning Logic in the Adopted Dataset
Overview
To further constrain multipolarities (G-record M field) and then use them to deduce Jπ for each level (L-record Jπ field).
Assignment Patterns
Assigning M1+E2 or (M1+E2) in the G-record M field:
-
Assign firm M1+E2 directly based on DCO/ADO and POL data. The cG M$ comment should cite the specific dataset:
cG M$from |g|g(|q)(DCO) and |g|g(|q)(POL) in dataset.
-
Assign firm M1+E2 from D+Q without POL when the level lifetime is short (M2 ruled out by RUL). The cG M$ comment should cite the dataset and note RUL:
cG M$D+Q from |g(|q) in dataset. M2 ruled out by RUL.
cG M$D+Q from |g|g(|q)(DCO) in dataset. M2 ruled out by RUL.
Use M1+E2 in cL J$ comments to deduce Jπ:
cL J$<G-energy>|g, M1+E2, to <Jπ>, <L-energy> level
cG M$D+Q from |g(|q) in dataset. M2 ruled out by RUL.
Use M1+E2, |DJ=1, in cL J$ comments to deduce Jπ:
<G-energy>|g, M1+E2, |DJ=1 to <Jπ>, <L-energy> level
cG M$from |g|g(|q)(DCO) and |g|g(|q)(POL) in dataset.
cG M$D+Q from |g|g(|q)(DCO) in dataset. M2 ruled out by RUL.
-
Assign tentative (M1+E2) from firm D+Q when the level scheme indicates Δπ=no:
cG M$D+Q from |g(|q) in dataset. |D|p=no from level scheme.
cG M$D+Q from |g|g(|q)(DCO) in dataset. |D|p=no from level scheme.
If D(+Q) is firm, the corresponding converted form is M1(+E2). The same logic applies to E1+M2.
Conversion Decision Table
| Individual G | Measurement | Adopted G | For G record M field | For L record Jπ field |
|---|
| M1+E2 | DCO stretched D, POL, w/wo δ | M1+E2 | | M1+E2, ΔJ=1, Δπ=no |
| M1(+E2) | DCO stretched D, POL, w/wo δ | M1(+E2) | | M1(+E2), ΔJ=1, Δπ=no |
| E1+M2 | DCO stretched D, POL, w/wo δ | E1+M2 | | E1+M2, ΔJ=1, Δπ=yes |
| E1(+M2) | DCO stretched D, POL, w/wo δ | E1(+M2) | | E1(+M2), ΔJ=1, Δπ=yes |
| D+Q | DCO stretched D with δ<1 | M1+E2 | M2 ruled out by RUL | M1+E2, ΔJ=1, Δπ=no |
| D+Q | DCO stretched D with δ<1 | (M1+E2) | Δπ=no from level scheme | D+Q, ΔJ=1 |
| D+Q | DCO stretched D with δ<1 | (E1+M2) | Δπ=yes from level scheme | D+Q, ΔJ=1 |
| D(+Q) | DCO stretched D with δ≈0 | (M1(+E2)) | Δπ=no from level scheme | D(+Q), ΔJ=1 |
| D(+Q) | DCO stretched D with δ≈0 | (E1(+M2)) | Δπ=yes from level scheme | D(+Q), ΔJ=1 |
| D+Q | DCO seems like Q with δ>1 | M1+E2 | M2 ruled out by RUL | M1+E2, ΔJ=0,1, Δπ=no |
| D+Q | DCO seems like Q with δ>1 | (M1+E2) | Δπ=no from level scheme | D+Q, ΔJ=0,1 |
| D+Q | DCO seems like Q with δ>1 | (E1+M2) | Δπ=yes from level scheme | D+Q, ΔJ=0,1 |
| D+Q | DCO consistent with ΔJ=0 and δ<1 | M1+E2 | M2 ruled out by RUL | M1+E2, Δπ=no, Avoid using ΔJ=0 |
| D+Q | DCO consistent with ΔJ=0 and δ<1 | (M1+E2) | Δπ=no from level scheme | Avoid using ΔJ=0 |
| D+Q | DCO consistent with ΔJ=0 and δ<1 | (E1+M2) | Δπ=yes from level scheme | Avoid using ΔJ=0 |
| D(+Q) | DCO consistent with ΔJ=0 and δ≈0 | (M1(+E2)) | Δπ=no from level scheme | Avoid using ΔJ=0 |
| D(+Q) | DCO consistent with ΔJ=0 and δ≈0 | (E1(+M2)) | Δπ=yes from level scheme | Avoid using ΔJ=0 |
| D+Q | γ(θ)/DCO mixed | M1+E2 | M2 ruled out by RUL | M1+E2, ΔJ=0,1, Δπ=no |
| D+Q | γ(θ)/DCO mixed | (M1+E2) | Δπ=no from level scheme | D+Q, ΔJ=0,1 |
| D+Q | γ(θ)/DCO mixed | (E1+M2) | Δπ=yes from level scheme | D+Q, ΔJ=0,1 |
| D(+Q) | γ(θ)/DCO mixed | (M1(+E2)) | Δπ=no from level scheme | D(+Q), ΔJ=0,1 |
| D(+Q) | γ(θ)/DCO mixed | (E1(+M2)) | Δπ=yes from level scheme | D(+Q), ΔJ=0,1 |
| | [M1,E2] | Purely from level scheme | Do not use to deduce Jπ |
Conversion Precedence Rules
If lifetime is available and rules out M2 by RUL, then D+Q can be converted to firm M1+E2.
If RUL does not rule out M2, then D+Q can be converted to tentative (M1+E2) if level scheme indicates Δπ=no.
RUL takes precedence over level scheme for this conversion.
If Δπ is unknown from level scheme or RUL does not rule out M2, keep the original multipolarity assignment with only D and Q labels.
Capture Transitions
Primary γ transitions from neutron/proton capture resonances are possibly dominated by the lowest multipoles (E1, M1, E2). Higher orders are suppressed.
- D including E1 or M1: ΔJ = 0, 1; Δπ = Yes or No
- E2: ΔJ = 2; Δπ = No
Examples: Deducing Jπ of a final level from multipolarity and Jπ of the initial level
Primary γ transition from 5/2+ Initial via D or E2:
- D {E1, M1}: Final 3/2±, 5/2±, 7/2±
- E2: Final 1/2+, 9/2+
- Combination: 1/2+, 3/2±, 5/2±, 7/2±, 9/2+
Primary γ transition from 7/2- Initial via D or E2:
- D {E1, M1}: Final 5/2±, 7/2±, 9/2±
- E2: Final 3/2-, 11/2-
- Combination: 3/2-, 5/2±, 7/2±, 9/2±, 11/2-
If two primary γ transitions from 5/2+ and 7/2-, the "AND" intersection of the above two sets:
- Jπ of the final level: 3/2-, 5/2±, 7/2±, 9/2+
Considering the multipolarity is not directly determined by experimental evidence, the final Jπ is put in parentheses to indicate the assumptions made:
- Adopted: (3/2-, 5/2±, 7/2±, 9/2+)
Spin and Parity Assignment Reasoning Logic in the Adopted Dataset
Scenario C: No Angular Distribution DCO Ratios or Mixing Ratios Given in Literature
Goal
Deduce the Jπ of a level by combining constraints from:
- Feeding transitions — γ rays populating the level (from capture resonances above)
- Deexciting transitions — γ rays depopulating the level (to lower levels below)
Multipolarity Selection Rules
| Transition Type | Apply | Condition |
|---|
| Primary feeding γ (from resonances) | D or E2 | Always |
| Deexciting γ (decay to lower levels) | D or Q | Long or unknown lifetime |
| Deexciting γ (decay to lower levels) | D or E2 | Short lifetime (RUL applies: M2 ruled out) |
Note: Primary γ = capture transition from neutron/proton resonance
Workflow Algorithm
FOR each feeding γ:
Apply D or E2 selection rules
IF feeding level has multi-valued Jπ (e.g., 1/2+,3/2+):
Calculate allowed Jπ for EACH value separately
Take OR (union) of results
ENDIF
ENDFOR
FOR each deexciting γ:
IF lifetime is short (RUL applies):
Apply D or E2 selection rules
ELSE:
Apply D or Q selection rules
ENDIF
ENDFOR
Take AND (intersection) of ALL constraints above
RESULT: Common Jπ values → Put in parentheses to indicate tentative assignment
Parentheses in ENSDF denote tentative assignments based on assumed multipolarities
Example 1: Fed by primary γ from 7/2-, 7/2+, and 5/2+
Fed by primary γ from 7/2- (D or E2):
3/2-, 5/2±, 7/2±, 9/2±, 11/2-
Fed by primary γ from 7/2+ (D or E2):
3/2+, 5/2±, 7/2±, 9/2±, 11/2+
Fed by primary γ from 5/2+ (D or E2):
1/2+, 3/2±, 5/2±, 7/2±, 9/2+
AND: 5/2±, 7/2±, 9/2+
Adopted: (5/2±, 7/2±, 9/2+)
Example 2: Fed by primary γ from 5/2-. Decay γ to 1/2+ and 5/2+ (Lifetime short, RUL applies, M2 ruled out)
Fed by primary γ (D or E2):
1/2-, 3/2±, 5/2±, 7/2±, 9/2-
Decay γ to 1/2+ (D or E2):
1/2±, 3/2±, 5/2+
Decay γ to 5/2+ (D or E2):
1/2+, 3/2±, 5/2±, 7/2±, 9/2+
AND: 3/2±, 5/2+
Adopted: (3/2±, 5/2+)
Example 3: Fed by primary γ from 7/2+. Decay γ to 5/2+ (Lifetime unknown, RUL does not apply, M2 allowed)
Fed by primary γ (D or E2):
3/2+, 5/2±, 7/2±, 9/2±, 11/2+
Decay γ to 5/2+ (D or Q):
1/2±, 3/2±, 5/2±, 7/2±, 9/2±
AND: 3/2+, 5/2±, 7/2±, 9/2±
Adopted: (3/2+, 5/2±, 7/2±, 9/2±)
Example 4: Fed by primary γ from 1/2+,3/2+ (multi-valued initial). Decay γ to 1/2+ and 3/2+ (Lifetime short, RUL applies, M2 ruled out)
Fed by primary γ from 1/2+,3/2+ (D or E2):
- From 1/2+ via D or E2: 1/2±, 3/2±, 5/2+
- From 3/2+ via D or E2: 1/2±, 3/2±, 5/2±, 7/2+
- OR (union): 1/2±, 3/2±, 5/2±, 7/2+
Decay γ to 1/2+ (D or E2):
1/2±, 3/2±, 5/2+
Decay γ to 3/2+ (D or E2):
1/2±, 3/2±, 5/2±, 7/2+
AND: 1/2±, 3/2±
Adopted: (1/2,3/2)
Note: When initial level has multiple J-π values (e.g., 1/2+,3/2+), calculate allowed final states for EACH initial value separately, then take OR (union) before applying AND with other constraints.
cL J$ Comment Style Rules
When writing primary transition lists in cL J$ comments:
- For primary transitions used to deduce Jπ of a level, do not use weak γ rays (Iγ < 5), γ rays with upper-limit intensity (
LT in the DRI field), γ rays with questionable placement (? in col 80), or γ rays to final levels with uncertain or multi-valued Jπ.
- List transitions in descending order of intensity, with the strongest first, to reflect the most probable deexcitation paths. If there are γ transitions to final levels with the same Jπ, include only the strongest one for that Jπ, as this is sufficient for Jπ deduction.
- Example for one γ transition:
cL J$primary transition <E_gamma1>|g to <Jπ1> g.s.
- Example for multiple γ transitions:
cL J$primary transitions: <E_gamma1>|g to <Jπ1> g.s., <E_gamma2>|g to <Jπ2>, <E_level2>, and <E_gamma3>|g to <Jπ3>, <E_level3>. Or, with specified intensities: cL J$primary transitions with I|g>10: <E_gamma1>|g to <Jπ1> <E_level1> and <E_gamma2>|g to <Jπ2>, <E_level2>. Or, with specified multipolarities: cL J$primary transitions: <E_gamma1>|g, D(+Q), to <Jπ1>, <E_level1> and <E_gamma2>|g, D(+Q), to <Jπ2>, <E_level2>.
- Use Oxford comma style in multi-transition lists and keep existing other Jπ arguments. Example:
cL J$spin=1:4 from |g(|q) in {+33}S(p,|g). Primary transitions: 4328.7|g to 2+, 2157.9 level, 6486.2|g to 0+ g.s., and 6025.3|g to 1+, 461.01 level.
