spin-parity-notation-instructions

name	spin-parity-notation-instructions
description	Use this skill as a reference guide for ENSDF spin-parity (Jπ) notation rules. Covers L-transfer field positioning at column 56, J-π assignment confidence levels using parentheses, single/multiple/range spin assignments, and critical parentheses placement rules. Suitable for writing J-π values in L-records or J$ comment lines.
argument-hint	["spin-parity expression or L-record line"]

ENSDF Spin-Parity Interpretation Reference

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.

L-Transfer Field Positioning

L-Transfer Field Positioning Rule

• L always starts from column 56 (EXACT rule for L transferred angular momentum fields)
• L=1 → 1 at column 56
• L=1+2 → 1 at column 56, +2 at columns 57-58
• L=1,2 → 1 at column 56, ,2 at columns 57-58
• ONLY the first L-value must be at column 56; subsequent values follow sequentially

L-Transfer from 0+ for J-π Assignment Rules

Physics mapping (single-nucleon transfer from a 0+ even-even target):

• j = L ± 1/2
• π = (−1)^L

L-Transfer values and corresponding J-π assignments:

• L=0 → J-π: 1/2+
• L=1 → J-π: 1/2-,3/2-
• L=2 → J-π: 3/2+,5/2+
• L=3 → J-π: 5/2-,7/2-
• L=4 → J-π: 7/2+,9/2+

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J-π Assignment Notation

Fundamental Rule

CRITICAL: J = spin; π = parity

• WITHOUT parentheses: Firm, well-established assignments (e.g., 3/2+, 7/2-, 0+, 5-)
• WITH parentheses: Less certain, tentative assignments (e.g., (3/2+), (7/2)-, 0(+), (5-))
• Parentheses indicate uncertainty in the assignment confidence, not the measurement precision
• With/without parentheses and the placement of parentheses are critical for conveying the confidence level of the assignment

Basic Single Assignments

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
1/2-	Firm	Firm	Impossible	Impossible	—
(9/2+)	Tentative	Tentative	Possible	Possible	—
7/2(+)	Firm	Tentative	Impossible	Possible	—
(5/2)-	Tentative	Firm	Possible	Impossible	—
(11/2)	Tentative	Unknown	Possible	Possible	—
+	Unknown	Firm	Possible	Impossible	—
(+)	Unknown	Tentative	Possible	Possible	—

Multiple Spin Assignments

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
1/2-,3/2-	Firm	Firm	Impossible	Impossible	1/2- or 3/2-
(5/2+,7/2+)	Tentative	Tentative	Possible	Possible	5/2+ or 7/2+ or low-probability other Jπ
(7/2,9/2)-	Tentative	Firm	Possible	Impossible	7/2- or 9/2- or low-probability other J-
1/2,3/2(+)	Firm	Tentative	Impossible	Possible	1/2± or 3/2+ or low-probability 3/2-
(1/2,3/2,5/2)-	Tentative	Firm	Possible	Impossible	1/2- or 3/2- or 5/2- or low-probability other J-
(3/2,5/2,7/2+)	Tentative	Mixed	Possible	Possible	3/2± or 5/2± or 7/2+ or low-probability other Jπ

Range Assignments

Range Parity Rules:

• A:B+ or A:B- — parity applies ONLY to endpoint B; intermediate values have ±
• (A:B)+ or (A:B)- — parity applies to ALL values A through B
• A:B(+) or A:B(-) — tentative parity applies ONLY to endpoint B

Column Definitions:

• Other Spin?: Whether spin values beyond those explicitly shown in the expansion are possible
• Other Parity?: Whether parity values beyond those explicitly shown in the expansion are possible (note: ± notation counts as showing both parities)

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
1/2:7/2	Firm	Unknown	Impossible	Possible	1/2± or 3/2± or 5/2± or 7/2±
(1/2:7/2)	Tentative	Unknown	Possible	Possible	1/2± or 3/2± or 5/2± or 7/2± or low-probability other Jπ
1/2+:7/2+	Firm	Mixed	Impossible	Impossible	1/2+ or 3/2± or 5/2± or 7/2+
1/2-:7/2+	Firm	Mixed	Impossible	Impossible	1/2- or 3/2± or 5/2± or 7/2+
1/2:7/2+	Firm	Mixed	Impossible	Impossible	1/2± or 3/2± or 5/2± or 7/2+
1/2+:7/2	Firm	Mixed	Impossible	Impossible	1/2+ or 3/2± or 5/2± or 7/2±
(1/2+:7/2+)	Tentative	Mixed	Possible	Possible	1/2+ or 3/2± or 5/2± or 7/2+ or low-probability other Jπ
1/2(+):7/2(+)	Firm	Tentative	Impossible	Possible	1/2+ or 3/2± or 5/2± or 7/2+ or low-probability 1/2-, 7/2-
(1/2:7/2+)	Tentative	Mixed	Possible	Possible	1/2± or 3/2± or 5/2± or 7/2+ or low-probability other Jπ
(1/2+:7/2)	Tentative	Mixed	Possible	Possible	1/2+ or 3/2± or 5/2± or 7/2± or low-probability other Jπ
1/2:7/2(+)	Firm	Tentative	Impossible	Possible	1/2± or 3/2± or 5/2± or 7/2+ or low-probability 7/2-
(1/2:7/2)+	Tentative	Firm	Possible	Impossible	1/2+ or 3/2+ or 5/2+ or 7/2+ or low-probability other J+
(1/2:7/2)(+)	Tentative	Tentative	Possible	Possible	1/2+ or 3/2+ or 5/2+ or 7/2+ or low-probability other Jπ
1/2(+),3/2(+),5/2(+),7/2(+)	Firm	Tentative	Impossible	Possible	1/2+ or 3/2+ or 5/2+ or 7/2+ or low-probability other 1/2-, 3/2-, 5/2-, 7/2-

Note: The last entry is too long for the J field (cols 23-39) and should be placed in the 2 L continuation record.

Mixed Confidence Patterns

Notation	Spin	Parity	Other Spin?	Other Parity?	Expands To
1/2+,3/2-	Firm	Firm	Impossible	Impossible	1/2+ or 3/2-
3/2-,(5/2-)	Mixed	Firm	Mixed	Impossible	3/2- or (5/2-)
(7/2)+,9/2+	Mixed	Mixed	Mixed	Mixed	(7/2)+ or 9/2+
1/2(+),3/2-	Firm	Mixed	Mixed	Mixed	1/2(+) or 3/2- or low-probability 1/2-
(5/2+,7/2-)	Tentative	Tentative	Possible	Possible	5/2+ or 7/2- or low-probability other Jπ
3/2,5/2,7/2	Firm	Unknown	Impossible	Possible	3/2± or 5/2± or 7/2±
(1/2,3/2,5/2)	Tentative	Unknown	Possible	Possible	1/2± or 3/2± or 5/2± or low-probability other Jπ

Critical Formatting Rules

• Comma separation for multiple possibilities within same confidence level
• Parentheses apply to the entire group when wrapping multiple values
• Do not include explicit parity on an item inside a grouped tentative list; if a subset has a different parity or confidence, split it out of the group
• Mixed notation is allowed by splitting: e.g., 1/2,3/2,5/2+ (first two tentative, parity unspecified; last firm positive)
• No spaces around commas in J-π field
• Exact reproduction required — never modify parentheses placement without experimental justification

Critical Parentheses Matching Rule

Spin-parity with/without parentheses convey different confidence levels. When creating J$ comments or adding values to J fields from reference data sources, ensure parentheses are preserved exactly as written in the source:

• Source shows 3/2 → Comment: J$3/2 from [reference] (NO parentheses)
• Source shows (3/2) → Comment: J$(3/2) from [reference] (single parentheses preserved)
• NEVER use double parentheses: J$((3/2)) is FORBIDDEN
• Examples: (1/2+), 1/2(+), 1/2+ represent different assignment confidence levels and the placement of parentheses must be matched accurately and precisely!

Additional Notation

Ranges: 1/2:7/2 expands to 1/2, 3/2, 5/2, 7/2. Lists: 3/2, 5/2 expands to set of both. Parity Inheritance: (1/2, 3/2)+ applies + parity to both inner items, i.e., (1/2)+, (3/2)+. Loose Matching: Parentheses () indicate tentative values.