The word "longing" is correct and can be used in written English.
You can use it when you want to express a strong feeling of wanting something or someone. For example, "The mother held her child in her arms, filled with longing for the days when he was a baby."
Exact(57)
Long – and longing.
Longing for retribution is longing for retribution.
And longing.
Libraries generate longing.
Grief, longing.
Goodbye to longing.
— Increased longing for community.
Sex, longing and loss?
There's time for longing".
Perhaps longing as well.
Readers are left longing for a sequel.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com