Spin Parity Notation Instructions

• 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+

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

Multiple Spin Assignments

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)

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

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.