--- name: gamma-selection-rules description: > Use this skill when deducing multipolarities for gamma transitions and then Jπ for nuclear levels by combining constraints from deexciting and feeding gamma transitions using electromagnetic selection rules. Applies D/E2 rules to primary capture transitions, D/E2 rules 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`. - DCO and ADO interpretation rules: `.github/docs/angular_correlations_DCO.md`. - γ-ray angular distribution, mixing ratios, and polarization: `.github/docs/gamma_angular_distribution_mixing_ratio_polarization.md`. - M and MR field notation: `.github/skills/multipolarity-mixing-ratio/SKILL.md`. --- ## Goal Deduce the multipolarity of γ-ray transitions from experimental data. Deduce the Jπ of levels by combining constraints from: - **Deexciting transitions** — γ rays depopulating the level (to lower-lying levels) - **Feeding transitions** — γ rays populating the level (from higher-lying levels) --- ## Multipolarity Assignment Reasoning Logic in Individual Datasets ### Scenario A: Only Mixing Ratios and Spins Given in Literature - If level scheme indicates ΔJ = 0 or 1, assign D+Q in M field. - If level scheme indicates ΔJ = 2, assign Q+O in M field. - If level scheme indicates ΔJ = 3, assign O in M field and note O+H and δ 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 (ΔJ = 1) transition yields $R_{DCO}(D)$. - Gating on a stretched quadrupole (ΔJ = 2) transition yields $R_{DCO}(Q)$. - Expected DCO values depend on experimental detection setups (see `.github/docs/angular_correlations_DCO.md`). The values below are for example purposes. **DCO Decision Rules** **If $R_{DCO}(D)$ ≈ 1.0 or $R_{DCO}(Q)$ ≈ 0.5:** - Transition is stretched dipole (ΔJ = 1) dominant. - Mark as **D**. **If $R_{DCO}(Q)$ ≈ 1.0 or $R_{DCO}(D)$ ≈ 2.0:** - Transition is stretched quadrupole (ΔJ = 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 (δ) and Level Scheme Spin Change (ΔJ) Based on the Step 1 classification: **For Transitions Marked D** - If δ is not given, assign D in M field. - If |δ| < 1 is given, assign D+Q in M field. **For Transitions Marked Q** - If δ is not given, assign Q in M field. - If |δ| < 1 is given, assign Q+O in M field. - Then look at spins, the level scheme should indicate ΔJ = 2; but if it indicates ΔJ = 1, assign D+Q in M field and flag this discrepancy for user review. - If |δ| > 1 is given, assign D+Q in M field because dipole is the weaker component. **For Transitions Marked ΔJ=0** - If δ is not given, assign D in M field and note `consistent with |DJ=0` in the cG comment after the DCO value. - If |δ| < 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 δ is not given, no need to assign M field. - If δ is given: - If level scheme indicates ΔJ = 0 or 1, assign D+Q in M field. - If level scheme indicates ΔJ = 2, assign Q+O in M field. - If level scheme indicates ΔJ = 3, assign O in M field and note O+H and δ value in cG M,MR comment. #### Step 3: Mixing Ratio Refinement - If δ is given and does not overlap with 0, D+Q or Q+O remains unchanged. - If δ 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). ### Conversion Decision Table | Individual G | Measurement | Adopted G | For G record M field | For L record Jπ field | | ------------ | -------------------------------- | --------- | ------------------------ | ------------------------------ | | M1 | DCO stretched D, POL | M1 | | M1, ΔJ=1, Δπ=no | | E1 | DCO stretched D, POL | E1 | | E1, ΔJ=1, Δπ=yes | | E2 | DCO stretched Q, POL | E2 | | E2, ΔJ=2, Δπ=no | | M2 | DCO stretched Q, POL | M2 | | M2, ΔJ=2, Δπ=yes | | Q | DCO stretched Q | E2 | M2 ruled out by RUL | E2, ΔJ=2, Δπ=no | | 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 A measured `D`, `Q`, `D+Q`, or `D(+Q)` assignment fixes the dipole/quadrupole composition and ΔJ, but leaves the electromagnetic character open. Resolve it with the first basis below that applies: 1. **RUL (measured lifetime), for assignments containing a Q component.** The transition-strength code (Java, run by humans) shows that the M2 partial half-life exceeds the recommended upper limit, so the Q component is E2 and Δπ=no follows, making the D component M1. Firm result: `Q` → `E2`, `D+Q` → `M1+E2`, `D(+Q)` → `M1(+E2)`. Add `M2 ruled out by RUL.` 2. **Firm Δπ from the level scheme.** Both level parities are firm, which fixes the character while ΔJ stays as measured. Because it rests on assumed parities, the result is tentative: - Δπ=no: `D` → `(M1)`, `Q` → `(E2)`, `D+Q` → `(M1+E2)`, `D(+Q)` → `(M1(+E2))`. - Δπ=yes: `D` → `(E1)`, `Q` → `(M2)`, `D+Q` → `(E1+M2)`, `D(+Q)` → `(E1(+M2))`. Add `|D|p=no from level scheme.` or `|D|p=yes from level scheme.` Write that Δπ value in parentheses when either connected level carries a tentative parity (`8(+)`, `(6+)`, `(1-)`): `|D|p=(yes)`, `|D|p=(no)`. With both parities firm, write it plain: `|D|p=yes`, `|D|p=no`. 3. **Neither basis applies.** Keep the measured assignment unconverted and add no clause. A basis-2 conversion is read off the parities of the two levels that the transition connects, so it holds only because those Jπ were already assumed. Quoting the converted `(E1)`, `(M1+E2)`, etc. back as evidence for either endpoint's Jπ is therefore circular. The `cL J$` argument must cite the measured assignment in its unconverted form that matches the converted one: `D, |DJ=1 from |g|g(|q)(ADO)` instead of the parity-derived `(E1)`, or `D+Q, |DJ=0,1 from |g|g(|q)(DCO)` instead of `(M1+E2)`. ### Comment Examples - `cG M$D+Q from |g(|q) in NSR_keynumber or Reaction_Dataset.` - `cG M$M1, |DJ=1, from |g|g(|q)(DCO) and |g|g(|q)(POL) in dataset.` - `cG M$E2, |DJ=2, from |g|g(|q)(DCO) and |g|g(|q)(POL) in dataset.` - `cG M$M1+E2, |DJ=1, from |g|g(|q)(DCO) and |g|g(|q)(POL) in dataset.` - `cG M$D+Q from |g(|q) in dataset. M2 ruled out by RUL.` - `cG M$D+Q, |DJ=1, from |g|g(|q)(DCO) in dataset. M2 ruled out by RUL.` - `cG M$D+Q from |g(|q) in dataset. |D|p=no from level scheme.` - `cG M$D+Q, |DJ=1, from |g|g(|q)(DCO) in dataset. |D|p=no from level scheme.` Use γ properties in `cL J$` comments to deduce Jπ: - `cL J$|g to , level` - `cL J$|g, M1+E2, to , level` - `cL J$|g, M1+E2, |DJ=1 to , level` - `cL J$|g, E2, |DJ=2 to , level` - `cL J$|g, D, |DJ=1 to , level` - `cL J$|g, Q, |DJ=2 to , level` If D(+Q) is firm, the corresponding converted form is M1(+E2). The same logic applies to E1+M2. Bracketed `[...]` multipolarities `[E1]`, `[M1,E2]`, or `[E2]` are solely deduced from level-scheme Jπ changes between the transition initial and final levels and need no provenance comment. --- ## Transitions γ transitions are assumed to be dominated by the three 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 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+ 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 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 #### Workflow Algorithm ```text 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 γ from 7/2-, 7/2+, and 5/2+ (Lifetime unknown, RUL does not apply) Fed by γ from 7/2- (D or E2): 3/2-, 5/2±, 7/2±, 9/2±, 11/2- Fed by γ from 7/2+ (D or E2): 3/2+, 5/2±, 7/2±, 9/2±, 11/2+ Fed by 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 γ from 5/2-. Decay γ to 1/2+ and 5/2+ (Lifetime short, RUL applies, M2 ruled out) Fed by γ from 5/2- (D or E2): 1/2-, 3/2±, 5/2±, 7/2±, 9/2- Decay γ to 1/2+ {firm D or E2}: 1/2±, 3/2±, 5/2+ Decay γ to 5/2+ {firm D or E2}: 1/2+, 3/2±, 5/2±, 7/2±, 9/2+ **AND:** 3/2±, 5/2+ Adopted: 3/2±, 5/2+ without parentheses. #### Example 3: Decay γ to 7/2+. Decay γ to 5/2+ (Lifetime unknown, RUL does not apply) Decay γ to 7/2+ (D or E2): 3/2+, 5/2±, 7/2±, 9/2±, 11/2+ Decay γ to 5/2+ (D or E2): 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 Jπ 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: 1. For gamma 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. Keep a weak γ ray that the user wants to include if it helps further constrain the Jπ deduction, listed with the other transitions. 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$|g to g.s.` Wrap between words, but keep a level energy with its `level` designator. 4. Example for multiple γ transitions: `cL J$|g to g.s.; |g to , ; |g to , .` One list, `;` between transitions, one final period: no `,` or `and` between transitions, and no period before the last one. Or, with specified intensities: `cL J$transitions with I|g>10: |g to ; |g to , .` Or, with specified multipolarities: `cL J$|g, D(+Q), to , ; |g, D(+Q), to , .` 5. List the γ transitions separately from other existing Jπ arguments with periods. Example: `cL J$spin= from |g(|q) in . |g to , ; |g to g.s.; |g to , .`