gamma-selection-rules

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:

• Mark as Mixed.

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.

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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:

1. 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.

2. 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.

3. 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.

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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+)

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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

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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.

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cL J$ Comment Style Rules

When writing primary transition lists in cL J$ comments:

1. 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.
2. 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.
3. Example for one γ transition: cL J$primary transition <E_gamma1>|g to <Jπ1> g.s.
4. Example for multiple γ transitions: cL J$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>.
5. 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.