--- 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. --- ## 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.` `cG M$M1+E2, |DJ=1, from |g|g(|q)(DCO) and |g|g(|q)(POL) in dataset.` 2. Assign firm M1+E2 from D+Q without POL when the level lifetime is short (M2 ruled out by RUL). The `cG M$` 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, |DJ=1, 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, M1+E2, to , 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, M1+E2, |DJ=1 to , level` `cG M$M1+E2, |DJ=1, from |g|g(|q)(DCO) and |g|g(|q)(POL) in dataset.` `cG M$D+Q, |DJ=1, 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, |DJ=1, 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$` comments: 1. For primary transitions used to deduce Jπ of a level, do not use weak γ rays (Iγ < 5), γ rays with upper-limit intensity (`LT` in the `DRI` field), γ rays with questionable placement (`?` in col 80), or γ rays to final levels with uncertain or multi-valued Jπ. 2. List transitions in descending order of intensity, with the strongest first, to reflect the most probable deexcitation paths. If there are γ transitions to final levels with the same Jπ, include only the strongest one for that Jπ, as this is sufficient for Jπ deduction. 3. Example for one γ transition: `cL J$primary transition |g to g.s.` 4. Example for multiple γ transitions: `cL J$primary transitions: |g to g.s., |g to , , and |g to , .` Or, with specified intensities: `cL J$primary transitions with I|g>10: |g to and |g to , .` Or, with specified multipolarities: `cL J$primary transitions: |g, D(+Q), to , and |g, D(+Q), to , .` 5. Use Oxford comma style in multi-transition lists and keep existing other Jπ arguments. Example: `cL J$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.`